Question

A tangent to the circle x2 + y= 5 at the point (–2, 1) intersect the ellipse  at the point A, B. If tangents to the ellipse at the point A and B intersect at point C. Find the coordinate of points C.

Solution

Correct option is

Equation of tangent to the circle x2 + y= 5 at point (–2, 1) is

  –2x + y – 5 = 0

 2x – y + 5 = 0                                      … (1)

Let point C be (h, k)

Equation of line AB as a chord of contact from the point C with respect to ellipse 

               … (2)

As equation (1) and (2) respects same line

  

  

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SIMILAR QUESTIONS

Q1

The equation of the tangent to the ellipse x2 + 16y2 = 16 making an angle of 600 with x-axis is

Q2

The equation of the ellipse whose foci are  and one of its directrix is 5x = 36.

Q3

Center of hyperbola 9x2 – 16y2 + 18x + 32y – 151 = 0 is

Q4

The equation of the ellipse whose centre is (2, –3), one of the foci is (3, –3) and the responding vertex is (4, –3) is

Q5

Find the eccentricity of the ellipse, whose foci are (–3, 4) and (3, –4) and which passes through the point (1, 2)

Q6

If  is a tangent to the ellipse , then find out the eccentric angle of the point of tangency.

Q7

For what value of λ dose the line y = x + λ touches the ellipse 9x2 + 16y2 = 144.

Q8

Find the equations of the tangents to the ellipse 3x2 + 4y2 = 12 which perpendicular to the line y + 2x = 4.

Q9

Find the equation of pair of tangents drawn from the point (1, 2) and (2, 1) to the ellipse .

Q10

If the line 3y = 3x + 1 is a normal to the ellipse , then find out the length of the minor axis of the ellipse.