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

Find the equation of the circle which touches both the axes and the straight line 4x+3y=6 in the first quadrant and lies below it.

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 (a) (x^2)/(40)+(y^2)/(10)=1 (b) (x^2)/5+(y^2)/8=1 (c) (x^2)/(10)+(y^2)/(40)=1 (d) (x^2)/(40)+(y^2)/(30)=1

The equation of the incircle of equilateral triangle A B C where B-=(2,0),C-=(4,0), and A lies in the fourth quadrant is: (a) x^2+y^2-6x+(2y)/(sqrt(3))+9=0 (b) x^2+y^2-6x-(2y)/(sqrt(3))+9=0 (c) x^2+y^2+6x+(2y)/(sqrt(3))+9=0 (d) none of these

The number of ordered pairs which satisfy the equation x^2+2xsin(x y)+1=0 are (where y in [0,2pi] ) 1 (b) 2 (c) 3 (d) 0

The equation of the line passing through the center and bisecting the chord 7x+y-1=0 of the ellipse (x^2)/1+(y^2)/7=1 is (a) x=y (b) 2x=y (c) x=2y (d) x+y=0

The locus of the centre of a circle which touches externally the circle x^2 + y^2-6x-6y+14 = 0 and also touches Y-axis, is given by the equation (a) x^2-6x-10y+14 = 0 (b) x^2-10x-6y + 14 = 0 (c) y^2+6x-10y+14-0 (d) y^2-10x-6y + 14 = 0

If the parabola y=(a-b)x^2+(b-c)x+(c-a) touches x- axis then the line ax+by+c=0 passes through a fixed point

The circle x^2 + y^2 - 4x + 6y + c = 0 touches x axis if

The number of triangles that the four lines y = x + 3, y = 2x + 3, y = 3x + 2, and y + x = 3 form is (a) 4 (b) 2 (c) 3 (d) 1

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) a^2 (b) b^2 (c) a^2b^2 (d) a^2+b^2