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Equation of directrix of parabola y2+4y+4x+2

WebFind the focus, directrix, and focal diameter of the parabola. y2 = 8x. write the equations of the parabola, the directrix, and the axis of symmetry. vertex: (-4,2) focus: (-4,6) if … WebStep 1: Standardize the given equation. The equation y 2 + 4 x + 4 y + k = 0 of the parabola is given. Standardize the given equation as follows: Add and subtract 4 from the Left-hand side. y 2 + 4 x + 4 y + k + 4 - 4 = 0 ⇒ y 2 + 4 y + 4 + 4 x + k - 4 = 0 ⇒ y + 2 2 = 4 - 4 x - k ⇒ y + 2 2 = - 4 x + - 4 + k 4 ... 1

The equation y^2 + 4x + 4y + k = 0 represents a parabola …

WebMar 28, 2024 · Equation of the directrix: y = -a Equation of axis: x = 0 Length of the latus rectum: 4a Focal distance of a point P (x, y): a + y 4. x2 = – 4ay Here, Coordinates of vertex: (0, 0) Coordinates of focus: (0, -a) Equation of the directrix: y = a Equation of axis: x = 0 Length of the latus rectum: 4a Focal distance of a point P (x, y): a – y WebJan 26, 2016 · The focus is at (1,3), the vertex is (2,3) and the directrix is at x = 3 Explanation: Reformulate the equation to have one variable on its own on the left hand side. In this case it should be x because y is the one that is raised to a power. y2 + 4x − 4y −8 = 0 4x = −y2 + 4y +8 x = − 1 4(y2 −4y − 8) cipher\\u0027s si https://reneevaughn.com

A parabola with focus (3, 0) and directrix x = –3. Points P and Q …

WebThen graph the parabola. y^2 = 4x; Find the vertex, focus, directrix, and axis of symmetry of the parabola (y - 1)^2 = 16x. Find directrix focus and axis for the parabola y^2 + 8x - 6y + 1 = 0. Find the focus and directrix of the parabola given by the equation y = 2 x^2 - 3 x + 10. Find the equation of a parabola with directrix x = 2 and focus ... WebQuestion: QUESTION 1 Find the focus and directrix of the parabola with the given equation. y^(2)=4x. QUESTION 1 Find the focus and directrix of the parabola with the given equation. y^(2)=4x. Expert Answer. Who are the experts? Experts are tested by Chegg as specialists in their subject area. We reviewed their content and use your … WebTherefore, the equation of the parabola can be written in vertex form as: (x-8)^2 = 4p (y-7) where p=3 is the distance from the vertex to the focus (or directrix). Simplifying this … cipher\\u0027s sh

A parabola can be drawn given a focus of (−8,0) and a directrix of y=−2 ...

Category:[Solved] Find the length of latus rectum of parabola y2 = - 24x

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Equation of directrix of parabola y2+4y+4x+2

Find the Properties y^2=4x Mathway

WebAny point (𝑥, 𝑦) on the parabola is equidistant to the focus and the directrix. We can express these distances using the distance formula, and we get √ ( (𝑥 − 9)² + (𝑦 − 0)²) = √ ( (𝑥 − 𝑥)² + (𝑦 − (−4))²) Simplifying and squaring both sides gives us (𝑥 − 9)² + 𝑦² = (𝑦 + 4)² Expanding the … WebJan 20, 2024 · Explanation: Write y2 + 4x −4y − 8 = 0 in the form of equation [1]: x(y) = − 1 4y2 + y + 2 [2] Matching values from equation [2] with variables in equation [1]: a = − 1 …

Equation of directrix of parabola y2+4y+4x+2

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WebOct 23, 2024 · The equation of the directrix of the parabola y2 + 4y + 4x + 2 = 0 is (a) x = -1 (b) x = 1 (c) x = - 3/2 (d) x = 3/2 LIVE Course for free Rated by 1 million+ students WebNov 24, 2024 · The standard equations of the parabola with the given coordinates of vertices, foci and equation of directrix are as follows: Vertex: (0, 0) Focus: (a, 0) Directrix: x = -a Equation of parabola: y 2 = 4ax Parametric Coordinates: (at2, 2at) Vertex: (0, 0) Focus: (-a, 0) Directrix: x = +a Equation of parabola: y 2 = -4ax

WebNov 26, 2016 · y2 = − 4x It is in the form y2 = − 4ax If it is so, then - Its vertex is (0,0) Its focus is ( − a,0) Its directrix is x = a Apply this in the given equation For better understanding the given equation can be written as y2 = 4 ⋅ ( −1) ⋅ x Then- Its vertex is (0,0) Its focus is ( − 1,0) Its directrix is x = 1 Answer link WebFeb 26, 2024 · Find the length of the latus rectum of the parabola whose focus is at (2, 3) and directrix is the line `x-4y+3=0` . asked Jan 20, 2024 in Parabola by AnantSharma ( …

WebThe equation of the parabola is Q. The equation of the circle which intersects circles x2+y2+x+2y+3=0,x2+y2+2x+4y+5=0 and x2+y2−7x−8y−9=0 at right angle, will be Parabola MATHEMATICS Watch in App WebThe given equation, y²+4y − 4x − 2 = 0 can be written as ; (y+2)² = 4 + 4x +2 = 4 (x+3/2) or Y² = 4aX , where Y = (y+2) , X = (x+3/2) and 4a = 4 (or a = 1 ) . Now, vertex V (x, y) is given by X= 0 = Y ==> (x, y) = (-3/2, -2) . Focus is given by F (x, y) i.e. X = a = 1 & Y = 0 ==> (x, y) = (-1/2, -2) and lastly the rectum = 4a = 4 . Gary Ward

WebThe directrix of the parabola y 2+4x+3=0 is A x− 43=0 B x+ 41=0 C x− 41=0 D x− 34=0 Medium Solution Verified by Toppr Correct option is C) The parabola is, y 2+4x+3=0 ⇒y 2=−4x−3=−4(x+ 43) Now comparing above equation with standard parabola, Y 2=−4aX Y=y,a=1,X=x+ 43 Hence d irectrix is X=a ⇒x+ 43=1 ⇒x− 41=0 Video Explanation Was …

WebGiven the focus (h,k) and the directrix y=mx+b, the equation for a parabola is (y - mx - b)^2 / (m^2 +1) = (x - h)^2 + (y - k)^2. Equivalently, you could put it in general form: x^2 + 2mxy + m^2 y^2 -2 [h (m^2 - 1) +mb]x -2 [k (m^2 + 1)^2 -b]y + (h^2 + k^2) (m^2 + 1) - b^2 = 0 At least, I think this last one is right. dialysis companies in usWebGiven an equation of a parabola, find the vertex, focus, and directrix. Draw the graph y 2 -4y+4=4x+4 Expert Answer 1st step All steps Final answer Step 1/3 Given is the … cipher\u0027s slWebGiven the focus (h,k) and the directrix y=mx+b, the equation for a parabola is (y - mx - b)^2 / (m^2 +1) = (x - h)^2 + (y - k)^2. Equivalently, you could put it in general form: x^2 + … dialysis company near meWebA parabola with focus (3, 0) and directrix x = –3. Points P and Q lie on the parabola and their ordinates are in the ratio 3 : 1. The point of intersection of tangents drawn at points P and Q lies on the parabola (1) y 2 = 16x (2) y 2 = 4x (3) y 2 = 8x (4) x 2 = 4y cipher\u0027s sjWebWrite the equation into the standard form of the equation of the parabola: x2 + 4x – 4y = 0.… A: Click to see the answer Q: Find the focus and directrix of the parabola with the given equation. 4) 9x2 = -5y A: Compare standard equation of parabola question_answer question_answer question_answer question_answer question_answer question_answer cipher\\u0027s smWebAlgebra Graph y^2=4x y2 = 4x y 2 = 4 x Rewrite the equation as 4x = y2 4 x = y 2. 4x = y2 4 x = y 2 Divide each term in 4x = y2 4 x = y 2 by 4 4 and simplify. Tap for more steps... dialysis company rankingsWebWe start by assuming a general point on the parabola (x,y) (x,y). Using the distance formula, we find that the distance between (x,y) (x,y) and the focus (-2,5) (−2,5) is \sqrt { … dialysis company fresenius