Conic Sections ...

The centre of a circle whose end points of a diameter are $$(-6,3)$$ and $$(6,4)$$ is

Length of latus rectum of the ellipse is 

The foci of ellipse are 

Length if semi latus rectum of ellipse $$x^2 + 4y^2 = 12$$ will be :

The hyperbola $$\dfrac{x^{2}}{a^{2}}-\dfrac{y^{2}}{b^{2}}=1$$ has its conjugate axis of length $$5$$ and passes through the point $$(2, 1)$$. The length of latus rectum is :

$$f(\displaystyle \mathrm{m}_{\mathrm{i}}, \frac{1}{\mathrm{m}_{\mathrm{i}}})$$ , $$\mathrm{i}=1,2,3,4$$ are four distinct points on the circle with centre origin, then value of $$\mathrm{m}_{1}\mathrm{m}_{2}\mathrm{m}_{3}\mathrm{m}_{4}$$ is equal to

lf the equation $$136 (x^{2}+y^{2})=(5x+3y+7)^{2}$$ represents a conic, then its length of latus rectum is

The graph of the curve $$x^2 + y^2 - 2xy - 8x - 8y + 32 = 0$$ falls wholly in the

A point $$P(x, y)$$ moves in $$XY$$ plane such that $$x = a\cos^2 \theta$$ and $$y = 2a \sin \theta$$, where $$\theta$$ is a parameter. The locus of the point $$P$$ is

Let P point on the circle $$x^2 + y^2 = 9$$, Q a point on the line $$7x + y + 3 = 0$$, and the perpendicular bisector of PQ be the line $$x - y + 1 = 0$$. Then the coordinate of P are