Conic Sections ...

The area of the triangle formed by the tangent and the normal to the parabola $${ y }^{ 2 }=4ax,$$ both drawn at the same end of the latus rectum and the axis of the parabola is

The latus rectum of the hyperbola $$16{x^2} - 9{y^2} = 144$$ is-

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

Length of the latus rectum of the hyperbola $$xy-3x-4y+8=0$$

The line $$y=mx+c$$ cut the circle $${x}^{2}+{y}^{2}={a}^{2}$$ in the distinct point $$A$$ and $$B$$. Equation of the circle having minimum radius that an be drawn through the points $$A$$ and $$B$$ is

Length of the latusrectum of the hyperbola $$xy-3x-4y+8=0$$ is 

Three sides of a triangle have the equations $$L_{r} = y - m_r x - C_{r} = 0; r = 1, 2, 3$$. Then $$\lambda L_{2}L_{3} + \mu L_{3}L_{1} + \gamma L_{1}L_{2} = 0$$. where $$\lambda \neq 0, \mu \neq 0, \gamma \neq 0$$, is the equation of circumcircle of triangle if

The equation $$14x^{2}-4xy+11y^{2}-44x-58y+71=0$$ represents

The equation of the circle passing through the points $$(4, 1), (6, 5)$$ and having the centre on the line $$4x+y-16=0$$ is 

The length of latus rectum of the parabola $$4y^{2}+3x+3y+1=0$$ is