The slopes of the common tanents of the ellipse 4x2+1y2=1
and the circle x2+y2=3
(d) none of these
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A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB+CD=AD+BC
Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.
PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T. Find the length TP.
Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.5y2−9x2=36
Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.9y2−4x2=36
The coordinates of the point AandB
are (a,0) and (−a,0),
respectively. If a point P
moves so that PA2−PB2=2k2,
is constant, then find the equation to the locus of the point P˙
A rod of length l
slides with its ends on two perpendicular lines. Find the locus of its midpoint.
If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.