## Question

### Solution

Correct option is The equation of any tangent to the ellipse  It meets the coordinate of axes at Let P(hk) be the mid-point of AB. Then  Since (i) touches the circle Therefore,   Hence the locus of P(hk) is  #### SIMILAR QUESTIONS

Q1

Find the equations of the tangents to the ellipse which are perpendicular to the line y + 2x = 4.

Q2

Find the locus of the foot of the perpendicular drawn from centre upon any tangent to the ellipse .

Q3

Find the locus of the points of the intersection of tangents to ellipse which make an angle θ.

Q4

Find the locus of the poles of tangents to with respect to the concentric ellipse .

Q5

Determine the equation of major and minor axes of the ellipse Also, find its centre, length of the latusrectum and eccentricity.

Q6

Find the locus of the centroid of an equilateral triangle inscribed in the ellipse Q7

If SY and S1Y1 be perpendiculars from the foci upon the tangent atP of an ellipse, then Y and Y1 lie on the auxiliary circle andSY.S1Y1 =

Q8

Find the condition on a and b for which two distinct chords of the ellipse passing through (a, –b) are bisected by the line x + y = b

Q9

Let P be a point on the ellipse , 0 < b < a. Let the line parallel to y-axis passes through P meet the circle at the point Q, such that P and Q are the same side of x-axis. For two positive  real numbers r and s, find the locus of the point Ron PQ such that PR : RQ = r : s as P varies over the ellipse.

Q10

The orbit of earth is an ellipse with eccentricity 1/60 with the sun at one focus the major axis being approximately 186 × 106 miles in length. Find the shortest and longest distance of the earth from the sun.