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 =
Equation of tangent at is
Equation of the perpendicular to (i) and passing through (ae, 0) is
For locus of Y, eliminate Ï• from equations (i) and (ii), for which squaring and adding (i) and (ii), we get
Hence locus of Y is the auxiliary circle. Similarly, as above we can prove that the locus of point Y1 is the auxiliary circle.
The extremities of a line segment of length l move in two fixed perpendicular straights lines. Find the locus of that point which divides this line segment in ratio 1 : 2.
Find the lengths and equations of the focal radii drawn from the point on the ellipse 25x2 + 16y2 = 1600.
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
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.