The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse. x2 + 9y2 = 9, meets the auxillary circle at the point M, then the area of the triangle with vertices at A, M and the origin O is
Equation of the ellipse is and of the auxillary circle is x2 + y2 = 9.
Equation of AB is .
y-coordinate of M is given by
[3(1 – y)]2 + y2 = 9
⇒ 10y2 – 18y = 0
Consider the two curves C1 : y2 = 4x ; C2 : x2 + y2 – 6x + 1, then
If F1 = (3, 0), F2 = (–3, 0) and P is any point on the curve 16x2 +25y2 = 400, then PF1 + PF2 equal
The locus of the points of intersection of the tangents at the extremities of the chords of the ellipse x2 + 2y2 = 6 which touch the ellipse x2 + 4y2 = 4 is
The normal at an end of a latus rectum of the ellipse passes through an end of the minor axis if
If an ellipse slides between two perpendicular straight line, then the locus of its center is
If the tangent at a point on the ellipse meets the auxillary circle in two points, the chords joining them subtends a right angle at the center; then the eccentricity of the ellipse is given by
The normal at a point P on the ellipse x2 + 4y2 = 16 meets the x-axis at Q, then locus of M intersects the latus rectums of the given ellipse at the points.
Let a and b be non-zero real numbers. Then the equation (ax2 + by2 + c)(x2 – 5xy + 6y2) = 0 represents
The pints of intersection of the two ellipse x2 + 2y2 – 6x – 12y + 23 = 0 and 4x2 + 2y2 – 20x – 12y + 35 = 0.
The tangent at any point P of the hyperbola makes an intercept of length p between the point of contact and the transverse axis of the hyperbola, p1, p2 are the lengths of the perpendiculars drawn from the foci on the normal at P, then