If the ellipse `(x^2)/4+y^2=1` meets the ellipse `x^2+(y^2)/(a^2)=1` at four distinct points and `a=b^2-5b+7,` then `b` does not lie in (a)`[4,5]` (b) `(-oo,2)uu(3,oo)` (c)`(-oo,0)` (d) `[2,3]`

Tangents are drawn from the point P(3, 4) to the ellipse x^2/9+y^2/4=1 touching the ellipse at points A and B.

On the ellipse 4x^2+9y^2=1, the points at which the tangents are parallel to the line 8x=9y are (a) (2/5,1/5) (b) (-2/5,1/5) (c) (-2/5,-1/5) (d) (2/5,-1/5)

For the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 and (x^(2))/(b^(2))+(y^(2))/(a^(2)) =1

if the line x- 2y = 12 is tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at the point (3,(-9)/(2)) then the length of the latusrectum of the ellipse is

f(x)=(x-2)|x-3| is monotonically increasing in (a) (-oo,5/2)uu(3,oo) (b) (5/2,oo) (c) (2,oo) (d) (-oo,3)

If the ellipse (x^2)/(a^2-7)+(y^2)/(13-5a)=1 is inscribed in a square of side length sqrt(2)a , then a is equal to (a) 6/5 (b) (-oo,-sqrt(7))uu(sqrt(7),(13)/5) (c) (-oo,-sqrt(7))uu((13)/5,sqrt(7),) (d)no such a exists

If (sqrt(3))b x+a y=2a b touches the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , then the eccentric angle of the point of contact is (a) pi/6 (b) pi/4 (c) pi/3 (d) pi/2

The length of major ofthe ellipse (5x-10)^2 +(5y+15)^2 = 1/4(3x-4y+7)^2 is

A tangent is drawn to the ellipse to cut the ellipse x^2/a^2+y^2/b^2=1 and to cut the ellipse x^2/c^2+y^2/d^2=1 at the points P and Q. If the tangents are at right angles, then the value of (a^2/c^2)+(b^2/d^2) is

If a tangent of slope 2 of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 is normal to the circle x^2+y^2+4x+1=0 , then the maximum value of a b is 4 (b) 2 (c) 1 (d) none of these