Conic Sections ...

The equation of the circle passing through the points of intersection of the lines $$2x+y=0,\ x+y+3=0$$ and $$x-2y=0$$ is

Length of the latus rectum of the parabola $$25 [(x- 2)^{2}+(y-3)^{2}]=(3x-4y+7)^2 $$ is :

The length of the latus rectum of the parabola $$x^{2}-4x-8y+12=0$$ is-

The equation of the circle of a radius $$5$$ in the first quadrant which touches the x-axis and the line $$3x-4y=0$$ is 

Equation of circle touching $$x=0, y=0$$ and $$x=4$$ is 

Find the equation of a circle whose center is (2,-1) and radius is 3 

The vertex and focus of a parabola are $$(-2,2),(-6,6)$$. Then its length of latus rectum is

The equation of the tangent to the curve y = 2sinx + sin2x at $$x=\frac { \pi  }{ 3 } $$ on it is 

The order of the differential equation of the family of parabolas whose length of latus rectum is fixed and axis is the X-axis 

$${ \cos }^{ 4 }\dfrac { \pi  }{ 8 } +{ \cos }^{ 4 }\dfrac { 3\pi  }{ 8 } +{ \cos }^{ 4 }\dfrac { 5\pi  }{ 8 } +{ \cos }^{ 4 }\dfrac { 7\pi  }{ 8 } =$$