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

The product of the slopes of the tangents to the ellipse 2x²+3y²=6 draw from the point (1, 2) 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 locus of the middle point of chords of the ellipse x²/a²+y²/b²=1   whose pole lies on the auxiliary circle is

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

The equation of the chord of the ellipse 2x²+3y²=6 having (1, -1) as its midpoint 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 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 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 total number of real tangents that can be drawn to the ellipse 3x²+5y²=32 and 25x²+9y²=450 passing through (3, 5) is