A to Z Exams

I: The locus of poles of chords of the ellipse x2/a2+y2/b2=1  which touch the parabola y2= 4px is p a2y2+b4x=0 II: The locus of poles of chords of the ellipse x2/a2+y2/b2=1  which touch the x2/α2+y2/β2=1 is α 2x2/a4+β2y2/b4=1

The chord of contact of tangents drawn from points on x2/a2+y2/b2=1 to the circle x2+ y2=c2 touches the ellipse

If the equation of the pair of tangents drawn from (1, 2) on the ellipse x2+2y2=2 is 3x2-4xy-y2+ax+by+c=0 then the ascending order of a, b, c is

The locus of the middle point of chords of the ellipse x2/a2+y2/b2=1   whose pole lies on the auxiliary circle is

The equation of the normal at a point hose eccentric angle is 3π/2+θ to the ellipse x2/9+y2/4=1 is

If the polar of (2, -1) with respect to the ellipse 3x2+4y2=12 is  ax+by+c=0 then the ascending order  of a, b, c is

The equation of ellipse whose focus is (0, √a2-b2), directrix is y=a2/√a2-b2 and eccentricity is √a2-b2/a is

The radius of the circle passing through the foci of the ellipse x2/16+y2/9=1 and having its center at (0, 3) is

The pole of the line y=x+2 e with respect to the ellipse x2+4y2-2x-6y-10=0 is

The locus of the poles of chords of  the ellipse x2/a2+y2/b2=1 which touch The locus of the poles w.r.t the ellipse x2/α2+y2/β2=1 is

The locus of the poles w.r.t the ellipse x2/a2+y2/b2=1 of tangents to its auxiliary circle is

The ordinate PN of P(a cos θ, b sin θ) on the ellipse x2/a2+y2/b2=1 meets the auxiliary circle at Q,. The locus of the point of intersection of normal at P and Q is

The equation of the auxiliary circle of x2/12+y2/18=1 is

If the variable line l1(x-a)+y=0 and l2(x+a)+y=0 are conjugate lines w. r. to the ellipse x2/a2+y2/b2=1. Then the locus of their point of intersection is

Pole of the line 2x+3y+4=0 w.r.to the ellipse x2/2+y2/4=1 is

The midpoint of a chord 4x+5y-13=0 of the ellipse 2x2+5y2=20 is

The tangent and normal to the ellipse 4x2+9y2 =36 at a point P on it meets the major axis in Q nd R respectively. If QR=4, then the eccentric angle of P is

If the line lx+my=1 is a normal to the ellipse x2/a2+y2/b2=1 then a2/l2-b2/m2=1

The points on the ellipse x2/25+y2/9=1 whose angles differ by a right angle are

If the lines 4x+3y-1=0,x-y+5=0 and kx+5y-3=0 are concurrent,then k is equal to

The locus of a point P for which the chord of contact of  x2/a2+y2/b2=1 touch the circle x2+y2=r2

The product of the slopes of the tangents to the ellipse 2x2+3y2=6 draw from the point (1, 2) is

The value of k if (1, 2) (k, -1) are conjugate points with respect to the ellipse 2x2+3y2=6 is

If 2x-y+3=0, 4x+ky+3=0 are conjugate with respect to the ellipse 5x2+6y2-15=0 then k=

The equation of the chord of the ellipse 2x2+3y2=6 having (1, -1) as its midpoint is

The total number of real tangents that can be drawn to the ellipse 3x2+5y2=32 and 25x2+9y2=450 passing through (3, 5) is

The locus of midpoint of the chord of the ellipse x2/a2+y2/b2=1 which pass through the fixed point  (h, k) is

If the chord of contact of the point (1, -2) with respect to the ellipse 4x2+5y2=20 is ax+by+c=0 then the ascending order  of a, b, c is

The tangents are drawn to the ellipse x2/a2+y2/b2=1 at point where it is intersected by the line lx+my+n=0. The point of intersection of tangents at these points is

The locus of the middle point of chords of the ellipse x2/a2+y2/b2=1   which are at a constant distance d from the centre of the ellipse is