A variable parabola y2=4ax,a (where a=−41) being the parameter, meets the curve y2+x−2=0 at two points. The locus of the point of intersecion of tangents at these points is
Let E1 and E2, be two ellipses whose centers are at the origin.The major axes of E1 and E2, lie along the x-axis and the y-axis, respectively. Let S be the circle x2+(y−1)2=2. The straight line x+ y =3 touches the curves S, E1 and E2 at P,Q and R, respectively. Suppose that PQ=PR=322.If e1 and e2 are the eccentricities of E1 and E2, respectively, then the correct expression(s) is(are):
Find the equation of the circle with radius 5 whose centre lies on x-axis and passes through the point (2,3)
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse 36x2+16y2=1.
An ellipse is drawn with major and minor axis of length 10 and 8 respectively. Using one focus a centre, a circle is drawn that is tangent to ellipse, with no part of the circle being outside the ellipse. The radius of the circle is (A) 3 (B) 2 (C) 22 (D) 5
Suppose that the foci of the ellipse 9x2+5y2=1 are (f1,0)and(f2,0) where f1>0andf2<0. Let P1andP2 be two parabolas with a common vertex at (0, 0) and with foci at (f1.0)and (2f_2 , 0), respectively. LetT1 be a tangent to P1 which passes through (2f2,0) and T2 be a tangents to P2 which passes through (f1,0) . If m1 is the slope of T1 and m2 is the slope of T2, then the value of (m121+m22) is