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.
Given PR : RQ = r : s
Squaring and adding, we get
Hence locus of R is
For what value of λ dose the line y = x + λ touches the ellipse
9x2 + 16y2 = 144.
Find the equations of the tangents to the ellipse which are perpendicular to the line y + 2x = 4.
Find the locus of the foot of the perpendicular drawn from centre upon any tangent to the ellipse .
Find the locus of the points of the intersection of tangents to ellipse which make an angle θ.
Find the locus of the poles of tangents to with respect to the concentric ellipse .
Determine the equation of major and minor axes of the ellipse
Also, find its centre, length of the latusrectum and eccentricity.
Find the locus of the centroid of an equilateral triangle inscribed in the ellipse
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 =
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.
Consider the family of circle x2 + y2 = r2, 2 < r < 5. If in the first quadrant the common tangent to a circle of the family and the ellipse 4x2 + 25y2 = 100 meets the coordinate axes at A and B, then find the equation of the locus of the mid point of AB.