The Equation Of A Circle Passing Through The Vertex The Extremities Of The Latus Rectum Of The Parabola y2 = 8x is

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Question

The equation of a circle passing through the vertex the extremities of the latus rectum of the parabola y² = 8x is

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Solution

Correct option is

x² + y² – 10x = 0

y² = 8x = 4ax, say.

Then a = 2. Ends of latus rectum are

A(a, 2a), B(a, –2a) A(2, 4), B(2, –4).

Also vertex is V(0, 0). Any circle through V is

x² + y² + 2gx +2fy = 0 …. (1)

putting A and B in (1),

5a² + 2ag + 4fa = 0 …. (2)

5a² + 2ag – 4fa = 0 …. (3)

(2), (3) 8fa = 0 f = 0

(2), (4) 5a² + 2ag = 0

Putting (4) and (6) in (1), x² + y² – 5ax = 0. Here

x² + y² – 10x = 0

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SIMILAR QUESTIONS

Q1

The locus of the mid-point of the line segment joining the focus to a moving point on the parabola y² = 4ax is another parabola with directrix

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Q2

The equation of common tangent to the curves y² = 8x and xy = –1 is

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Q3

From the point (–1, 2) tangent lines are drawn to the parabola y² = 4x, then the equation of chord of contact is

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Q4

For the above problem, the area of triangle formed by chord of contact and the tangents is given by

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Q5

A point moves on the parabola y² = 4ax. Its distance from the focus is minimum for the following value(s) of x.

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Q6

The line x – y + 2 = 0 touches the parabola y² = 8x at the point

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Q7

If t is the parameter for one end of a focal chord of the parabola y² = 4ax, then its length is

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Q8

The point on the parabola y² = 8x at which the normal is inclined at 60⁰ to the x-axis has the coordinates

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Q9

The length of the latus rectum of the parabola 9x² – 6x + 36y + 19 = 0 is

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Q10

If the parabola y² = 4ax passes through the pint (1, –2), then the tangent at this point is

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