Equation Of The Parabola Whose Axis Is y = X distance From Origin To Vertex Is  and Distance Form Origin To Focus Is , Is (Focus And Vertex Lie In Ist Quadrant) :

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Question

Equation of the parabola whose axis is y = x distance from origin to vertex is  and distance form origin to focus is , is (Focus and vertex lie in Ist quadrant) :

Solution

Correct option is

(x – y)2 = 8(x + y – 2)

The equation of the axis of the parabola is

  

 A is (1, 1) and S is (2, 2) and foot of dirctrix be Z, then A is mid-point of SZ

Equation of directrix is

By definition if P(x, y) be any point on the parabola then SP = PM

or  

       2[x2 + y2 – 4x – 4y + 8] = (x + y)2

or       x2 + y2 – 2xy = 8(x + y – 2).

                                                            

Testing

SIMILAR QUESTIONS

Q1

The equation of circle touching the parabola y2 = 4x at the point  (1, –2) and passing through origin is

Q2

The vertex of a parabola is the point (a, b) and latus-rectum is of length l. If the axis of the parabola is along the positive direction of y-axis. Then its equation is

Q3

Slope of common tangent to parabolas y2 = 4x and x2 = 8y is

Q4

If a focal chord with positive slope of the parabola y2 = 16xtouches the circle x2 + y2 – 12+ 34 = 0, then m is

Q5

If 2y = x + 24 is a tangent to parabola y2 = 24x, then its distance from parallel normal is

Q6

PQ is a focal chord of the parabola y2 = 4axO is the origin. Find the coordinates of the centroid, G, of triangle OPQ and hence find the locus of G as PQ varies.

Q7

Find the shortest distance between the circle x2 + y2 – 24y + 128 = 0 and the parabola y2 = 4x.

Q8

The equation of the directrix of the parabola y2 + 4y + 4x + 2 = 0 is  

Q9

If the line x – 1 = 0 is the directrix of the parabola y– ky + 8 = 0, then one of the of the value of k is

  

Q10

The focal chord of y2 = 16x is tangent to (x – 6)2 + y2 = 2, then the possible values of the slope of this chord, are