Tangents are drawn to the hyperbola 4x2−y2=36 at the points P and Q. If these tangents intersect at the point T(0,3) then the area (in sq units) of △PTQ is
Two rods are rotating about two fixed points in opposite directions. If they start from their position of coincidence and one rotates at the rate double that of the other, then find the locus of point of the intersection of the two rods.
If e1and e2 are respectively the eccentricities of the ellipse 18x2+4y2=1 and the hyperbola 9x2−4y2=1, then the relation between e1and e2 is a.2e12+e22=3 b. e12+2e22=3 c. 2e12+e22=3 d. e12+3e22=2
Find the eccentricity, coordinates of the foci, equations of directrices and length of the latus rectum of the hyperbola 16x2−9y2=144
PQ and RS are two perpendicular chords of the rectangular hyperbola xy=c2˙ If C is the center of the rectangular hyperbola, then find the value of product of the slopes of CP,CQ,CR, and CS˙
OA and OB are fixed straight lines, P is any point and PM and PN are the perpendiculars from P on OAandOB, respectively. Find the locus of P if the quadrilateral OMPN is of constant area.