If three parabols touch all the lines x=0,y=0 and x+y=2, then maximum area of the triangle formed by joining their foci is
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Find the center, foci, the length of the axes, and the eccentricity of the ellipse 2x2+3y2−4x−12y+13=0
Find the equation of the circle passing through the points (4,1) and (6,5) and whose centre is on the line 4x+y=16
Find the center and radius of the circle x2+y2−4x−8y−45=0
Find the number of rational points on the ellipse 9x2+4y2=1.
Prove that any point on the ellipse whose foci are (−1,0)
and eccentricity is 21
be a point on the ellipse a2x2+b2y2=1
of eccentricity e˙
are the vertices and S,S
are the foci of the ellipse, then find the ratio area PSS′′
: area APAprime˙
Find the coordinates of the focus axis of the parabola, the equation of directrix and the length of the latus rectum for the parabola x2 =−16y.
An ellipse passes through the point (4,−1)
and touches the line x+4y−10=0
. Find its equation if its axes coincide with the coordinate axes.