Let a tangent to the curve `9x^2 +16y^2 = 144`, intersects the coordinate axes at A and B. Then the minimum length of the line segment AB is

Let S be the circle in the x y -plane defined by the equation x^2+y^2=4. (For Ques. No 15 and 16) Let P be a point on the circle S with both coordinates being positive. Let the tangent to S at P intersect the coordinate axes at the points M and N . Then, the mid-point of the line segment M N must lie on the curve (x+y)^2=3x y (b) x^(2//3)+y^(2//3)=2^(4//3) (c) x^2+y^2=2x y (d) x^2+y^2=x^2y^2

If any tangent to the ellipse 25x^(2)+9y^2=225 meets the coordinate axes at A and B such that OA = OB then , the length AB is equal to (where , O is the origin)

The equation of a tangent to the hyperbola 9x^2 - 12y^2 = 144 parallel to the line x- y=5 is:

The line passing through the extremity A of major axis and extremity B of the minor axes of the ellipse 9x^2 + 16y^2 = 144 meets the circle x^2+ y^2 =16 at the point P. Then the area of the triangle OAP, O being the origin (in square units) is

The tangent to the ellipse 3x^2 + 16y^2 = 12 , at the point (1, 3/4) , intersects the curve y + x = 0 at: