Tangent are drawn from any point on the hyperbola to the circle x2 + y2 = 9. If the locus of the mid-point of the chord of contact is
Equation of the chord of contact of a point on the hyperbola is with respect to the circle is
Let M(h, k) be the mid-point of (1), then equation of (1) in terms of the mid-point is
hx + ky = h2 + k2
Since (1) and (2) represent the same line.
Locus of (h, k) is
or 4(x2 + y2)2 = 36x2 – 81y2
which is same as a(x2 + y2)2 = bx2 – cy2
a = 4, b = 36, c = 81
a2 + b2 + c2 = 16 + 1296 + 6561 = 7873.
Find the locus of the mid-points of the chord of the parabola y2 = 4ax which subtend a right angle at the vertex.
If the parabola C and D intersect at a point A on the line L1, then equation of the tangent point L at A to the parabola D is
If a > 0, the angle subtended by the chord AB at the vertex of the parabola C is
P is a point on the circle C, the perpendicular PQ to the major axis of the ellipse E meets the ellipse at M, then is equal to
Equation of the diameter of the ellipse E conjugate to the diameter respected by L is
If R is the point of intersection of the line L with the line x = 1, then
If L is the chord of contact of the hyperbola H, then the equation of the corresponding pair of tangents is
If R is the point of intersection of the tangents to H at the extremities of the chord L, then equation of the chord contact of R with respect to the parabola P is
If the chord of contact of R with respect to the parabola Pmeets the parabola at T and T’, S is the focus of the parabola, then Area of the triangle STT’ is equal to
If l is the length of the intercept made by a common tangent to the circle x2 + y2 = 16 and the ellipse , on the coordinate axes, then 81l2+ 3 is equal to