An ellipse with major and minor axes lengths `2a` and `2b ,` respectively, touches the coordinate axes in the first quadrant. If the foci are `(x_1, y_1)a n d(x_2, y_2)` , then the value of `x_1x_2` and `y_1y_2` is a) -3`a^2` (b) `b^2` (c) `a^2b^2` (d) `a^2+b^2`

If y=a^(x)b^(2x-1) , then the value of (d^(2)y)/(dx^(2)) is -

The coordinates of the centre of the circle 2x^(2)+2y^(2) + ax + by + c= 0 are (3, - 4), find a and b.

If the tangents and normals at the extremities of a focal chord of a parabola intersect at (x_1,y_1) and (x_2,y_2), respectively, then (a) x_1=y_2 (b) x_1=y_1 (c) y_1=y_2 (d) x_2=y_1

If y=3^(x-1)+3^(-x-1) , then the least value of y is (a) 2 (b) 6 (c) 2//3 (d) 3//2

If d/dx ((1+x^2 + x^4)/(1+x+x^2)) = ax + b , then the values of a and b are

The equation of the circle which touches the axes of coordinates and the line x/3+y/4=1 and whose center lies in the first quadrant is x^2+y^2-2c x-2c y+c^2=0 , where c is (a) 1 (b) 2 (c) 3 (d) 6

A tangent having slope of -4/3 to the ellipse (x^2)/(18)+(y^2)/(32)=1 intersects the major and minor axes at points A and B , respectively. If C is the center of the ellipse, then find area of triangle A B Cdot

If a ,b , a n dc are in G.P. and x ,y , respectively, are the arithmetic means between a ,b ,a n db ,c , then the value of a/x+c/y is 1 b. 2 c. 1//2 d. none of these

If the chords of contact of tangents from two poinst (x_1, y_1) and (x_2, y_2) to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 are at right angles, then find the value of (x_1x_2)/(y_1y_2)dot

Consider a circle x^2+y^2+a x+b y+c=0 lying completely in the first quadrant. If m_1a n dm_2 are the maximum and minimum values of y/x for all ordered pairs (x ,y) on the circumference of the circle, then the value of (m_1+m_2) is (a) (a^2-4c)/(b^2-4c) (b) (2a b)/(b^2-4c) (c) (2a b)/(4c-b^2) (d) (2a b)/(b^2-4a c)