The equation of the ellipse whose axes are coincident with the coordinates axes and which touches the straight lines `3x-2y-20=0` and `x+6y-20=0` is `(x^2)/(40)+(y^2)/(10)=1` (b) `(x^2)/5+(y^2)/8=1` `(x^2)/(10)+(y^2)/(40)=1` (d) `(x^2)/(40)+(y^2)/(30)=1`

The pair of straight lines x+2y-1=0,x+2y-5=0 are.

Find the equation of the straight line which parallel with 3x+2y-6=0 and forms a triangle of area 21 square units with the straight lines x-2y=0 and y-2x=0.

Find the coordinates of the centroid of the triangle, formed by the lines x+2y-5=0, y+2x-7=0 and x-y+1=0 .

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

In the standard ellipse, the lines joining the ends of the minor axis to one focus are at right angles. The distance between the focus and the nearer vertex is sqrt(10) - sqrt(5) . The equation of the ellipse (a) (x^(2))/(36) +(y^(2))/(18) = 1 (b) (x^(2))/(40)+(y^(2))/(20) = 1 (c) (x^(2))/(20) +(y^(2))/(10) = 1 (d) (x^(2))/(10)+(y^(2))/(5) =1

Find the equation of the tangent to the ellipse 2x^(2)+3y^(2)=30 , which are parallel to the straight line x+y+18=0

Find the equations of the tangents to the ellipse 2x^2 + 3y^2 = 30 , which are parallel to the straight line x + y + 18 = 0.

Find the equation of the ellipse (referred to its axes as the axes of x and y , respectively) whose foci are (+-2,0) and eccentricity is 1/2

The equation of the circle whose diameter is the common chord of the circles x^2+y^2+3x+2y+1=0 and x^2+y^2+3x+4y+2=0 is

Find the maximum area of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 which touches the line y=3x+2.