Conic Sections ...

$$S_{1}$$ and $$S_{2}$$ are the foci of an ellipse of major axis of length 10 units, and P is any point on the ellipse such that the perimeter or triangle $$PS_{1}S_{2}$$ is 15. Then the eccentricity of the ellipse is

$$Center\quad of\quad the\quad hyperbola\quad { x }^{ 2 }+4{ y }^{ 2 }+6xy+8x-2y+7=0\quad is\quad $$

'O' is the vertex of the parabola $${ y }^{ 2 }=8x$$ and L is the upper end of the latus rectum. If LH is drawn perpendicular to OL meeting OX in H, then the length of the double ordinate through H is $$\lambda \sqrt { 5 } $$ where $$\lambda $$ is equal to 

Which of the following equations does not represent a hyperbola?

The set of points $$(x, y)$$ whose distance from the line $$y = 2x + 2$$ is the same as the distance from $$(2, 0)$$ is a parabola. This parabola is congruent to the parabola in standard form $$y = Kx^{2}$$ for some $$K$$ which is equal to

From the point $$A\left(0,3\right)$$ on the circle $${x}^{2}-4x+{\left(y-3\right)}^{2}=0$$ a chord $$AB$$ is drawn and extended to a point $$M$$ such that $$AM=2AB$$.The locus is

The line $$2x + y = 1$$ is tangent to the hyperbola $$\displaystyle \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$$. If this line passes through the point of intersection of the nearest directrix and the x-axis, then eccentricity of the hyperbola.

The equation of the circle having the lines $$x^2 + 2xy + 3x + 6y = 0$$ as its normals and having size just sufficient to contain the circle $$x (x - 4) + y(y - 3) = 0$$ is

$$LL^1$$ is the latus rectum of an ellipse and $$\Delta S^1LL^1$$ is an equilateral triangle. Then $$e=?$$

The normal at $$ P(8, 8)$$ to the parabola $$y^2=8x$$ cuts it again at Q then PQ =