If the chords of contact of tangents from two poinst (x1,y1) and (x2,y2) to the ellipse a2x2+b2y2=1 are at right angles, then find the value of y1y2x1x2˙
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If the coordinates of a variable point P
is a variable quantity, then find the locus of P˙
are three non-collinear points such that x12+y12=x22+y22=x32+y32,
then prove that x1sin2A+x2sin2B+x3sin2C=y1sin2A+y2sin2B+y3sin2C=0.
Find the centre and radius of the circlesx2+y2−8x+10y−12=0
Shift the origin to a suitable point so that the equation y2+4y+8x−2=0
will not contain a term in y
and the constant term.
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.49x2+36y2=1
Find the equation of the parabola that satisfies the given conditions:Focus (0,3); directrix y=3
Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.16x2−9y2=576