Section Formula & Conic Sections - Practice Questions & MCQ

Let $O$ be the vertex and $Q$ be any point on the parabola, $x^2=8y$. If the point $P$ divides the line segment $OQ$ internally in the ratio $1:3$, then the locus of $P$ is :

If the line 2x + y = k passes through the point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio 3 : 2, then k equals:

The point diametrically opposite to the point $P(1,0)$ on the circle $x^2+y^2+2x+4y-3=0$ is

Using section formula find the foot of perpendicular drawn from the point (2,3) to the line joining the points (2,0) and $(\frac{8}{13},\frac{12}{13})$

Let $\alpha ,\beta ,\gamma ,\delta \in \mathbb{Z}$ and let $\mathrm{A}(\alpha ,\beta ),\mathrm{B}(1,0),\mathrm{C}(\gamma ,\delta )$ and $\mathrm{D}(1,2)$ be the vertices of a parallelogram $\mathrm{ABCD}$. If $\mathrm{AB}=\sqrt{10}$ and the points $\mathrm{A}$ and $\mathrm{C}$ lie on the line $3\mathrm{y}=2\mathrm{x}+1$, then $2(\alpha +\beta +\gamma +\delta )$ is equal to

$\text{ Find the mid point of line segment }AB\text{ where }A=(3,5)\text{ and }B=(2,7)$

If M (1,2)  is the midpoint of the line joining A (3,-7 ) and B(x,y ) then find the value of $|x_1-y_1|$

If (a, 0), (3, a), (7,4), (9, -1), in order are 4 vertices of a parallelogram, then the value of a is