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# Section Formula & Conic Sections - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

## Quick Facts

• Section Formula is considered one the most difficult concept.

• 21 Questions around this concept.

## Solve by difficulty

Let O be the vertex and Q be any point on the parabola, x2 = 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:

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

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

## Concepts Covered - 1

Section Formula

Section Formula

1. Internal division

The coordinates of the point P (x, y) dividing the line segment joining the two points A (x1, y1) and B  (x2, y2) internally in the ratio m : n is given by

$\\\mathrm{\mathbf{x=\frac{mx_2+nx_1}{m+n},\;\;y=\frac{my_2+ny_1}{m+n}}}$

Note:

If P is the mid point of the line segment AB, then ratio become equals, i.e. m = n, in this case, coordinates of point P is

$\\\mathrm{\mathbf{x=\frac{x_1+x_2}{2},\;\;y=\frac{y_1+y_2}{2}}}$

1. External Division

The coordinates of the point P (x, y) dividing the line segment joining the two points A (x1, y1) and B  (x2, y2) externally in the ratio m : n is given by

$\\\mathrm{\mathbf{x=\frac{mx_2-nx_1}{m-n},\;\;y=\frac{my_2-ny_1}{m-n}}}$

NOTE:

• If the ratio in which a given line segment is divided, is to be determined, then sometimes, for convenience (instead of taking the ratio m : n)  we take the ratio λ : 1 and apply the formula for internal division $\left(\frac{\lambda x_{2}+x_{1}}{\lambda+1}, \frac{\lambda y_{2}+y_{1}}{\lambda+1}\right).$

• If the value of λ > 0,  it is an internal division, otherwise it is an external division (i.e. when λ < 0 )

•

## Study it with Videos

Section Formula

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## Books

### Reference Books

#### Section Formula

Mathematics for Joint Entrance Examination JEE (Advanced) : Coordinate Geometry

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