Let x2+y2−2x−2y−2=0 and x2+y2−6x−6y+14=0 are two circles C1,C2 are the centre of circles and circles intersect at P,Q find the area of quadrilateral C1PC2Q (A) 12 (B) 6 (C) 8 (D) 4
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The locus a point P(α,β) moving under the condition that the line y=αx+β is a tangent to the hyperbola a2x2−b2y2=1 is (A) a parabola (B) an ellipse (C) a hyperbola (D) a circle
Find the coordinates of the foci, the vertices the eccentricity and the length of latus rectum of the hyperbola 9y2−4x2=36
If the equation (5x−1)2+(5y−2)2=(λ2−2λ+1)(3x+4y−1)2
represents an ellipse, then find values of λ˙
The moon travels an elliptical path with Earth as one focus. The maximum distance from the moon to the earth is 405, 500 km and the minimum distance is 363,300 km. What is the eccentricity of the orbit?
An ellipse slides between two perpendicular straight lines. Then identify the locus of its center.
If the tangent at any point of the ellipse a3x2+b2y2=1
makes an angle α
with the major axis and an angle β
with the focal radius of the point of contact, then show that the eccentricity of the ellipse is given by e=cosαcosβ
touches the ellipse a2x2+b2y2=1
, then find the eccentric angle θ
of point of contact.
Prove that the chords of contact of pairs of perpendicular tangents to the ellipse a2x2+b2y2=1 touch another fixed ellipse.