Conic Sections ...

The length of latus rectum of the parabola whose parametric equations are $$ x = t^{2} + t + 1$$, $$y = t^{2}-  t + 1$$, where $$t \in R$$, is equal to?

For the variable, the locus of the point of intersection of the lines $$3tx-2y+6t=0$$ and $$3x+2ty-6=0$$ is

If the line $$3x+4y=24$$ and $$4x+3y=24$$ intersects the coordinates axes at $$A,B,C$$ and $$D$$, then the equation of the circle passing through these $$4$$ points  is

The equation of a straight line drawn through the focus of the parabola $$y^2=-4x$$ at an angle of $$120^o$$ to the $$x$$-axis is.

Find the length of latus rectum of the parabola
$$(a^{2}+b^{2})(x^{2}+y^{2})=(bx+ay-ab)^{2}$$

The locus of the point $$(h,k)$$, if the point $$(\sqrt{3h}, \sqrt{3k + 2})$$  lies on the line $$x - y - 1 = 0$$, is a ?

A circle touches the $$x$$-axis and also touches the circle with centre $$(0, 3)$$ and radius $$2$$. The locus of the centre of the circle is -

A point $$(\alpha, \beta)$$ lies on a circle $$x^2+y^2=1$$, then locus of the point $$(3\alpha +2\beta)$$ is a$$/$$an.

Find the equation of the circle that passes through the points $$(0,6),(0,0)$$ and $$(8,0)$$

A circle and a parabola intersect at four points $$(x_1 , y_1), (x_2 , y_2), (x_3 , y_3)$$ and $$(x_4 , y_4)$$. Then $$y_1 + y_2 + y_3 + y_4$$ is equal to