The locus of the point of intersection of tangents to the ellipse , which make complementary angles with x-axis, is
The equation of any tangent to the ellipse
Let P(h, k) be the point of intersection of tangents.
If (i) passes through P(h, k), then
This gives two values of m, say m1 and m2. These values represent the slopes of the tangents passing through P.
If the tangents drawn from P make complementary angles with x-axis, then
Hence, the locus of (h, k) is x2 - y2 = a2 – b2.
If α – β = constant, then the locus of the point of intersection of tangents at to the ellipse
Let S(3, 4) and S’(9, 12) be two foci of an ellipse. If the coordinates of the foot of the perpendicular from focus S to a tangent to the ellipse is (1, –4), then the eccentricity of the ellipse is
Let S and S’ be two foci of the ellipse . If a circle described on SS’ as diameter intersects the ellipse in real and distinct points, then the eccentricity e of the ellipse satisfies
If PSQ is a focal chord of the ellipse , then the harmonic mean of SP and SQ is
If PSQ is a focal chord of the ellipse 16x2 + 25y2 = 400 such that SP = 8, then SQ =
If S and S’ are two focii of the ellipse 16x2 + 25y2 = 400 andPSQ is a focal chord such that SP = 16, then S’Q =
Tangent at a point on the ellipse is drawn which cuts the coordinates axes at A and B. The minimum area of the triangleOAB is (O being origin)
The locus of the foot of the perpendicular from the foci on any tangent to the ellipse
The locus of the point of intersection of tangents to the ellipse at the points whose eccentric angles differ by is
The locus of the foot of the perpendicular drawn from the centre of the ellipse on any tangent is