Family of Lines - Practice Questions & MCQ

If the lines 3y + 4x = 1, y = x + 5 and 5y + bx = 3 are concurrent, then the value of b is

The base BC of a triangle ABC contains the points $\mathrm{P}\left(\mathrm{p}_1, \mathrm{q}_1\right)$ and $\mathrm{Q}\left(\mathrm{p}_2, \mathrm{q}_2\right)$ and the equation of sides AB and AC are $\mathrm{p}_1 \mathrm{x}+\mathrm{q}_1 \mathrm{y}=1$ and $\mathrm{q}_2 \mathrm{x}+\mathrm{p}_2 \mathrm{y}=1$ respectively. The equation of AQ is and $\left(\mathrm{kp}_2 \mathrm{q}_2-1\right)\left(\mathrm{p}_1 \mathrm{x}+\mathrm{q}_1 \mathrm{y}-1\right)=\left(\mathrm{p}_1 \mathrm{p}_2+\mathrm{q}_1 \mathrm{q}_2-1\right)\left(\mathrm{q}_2 \mathrm{x}+\mathrm{p}_2 \mathrm{y}-1\right)$ where $\mathrm{k}=$.

A variable line drawn through the point of intersection of the straight lines $\frac{\mathrm{x}}{\mathrm{a}}+\frac{\mathrm{y}}{\mathrm{b}}=1$ and $\frac{\mathrm{x}}{\mathrm{b}}+\frac{\mathrm{y}}{\mathrm{a}}=1$ meets the co-ordinate axes in $\mathrm{A} \& \mathrm{~B}$. Find the locus of the mid point of AB .

A line which makes an acute angle with the positive direction of the  is drawn through the point , to cut the curve at   and . The lengths of the segments   and are numerical values of the roots of the equation       where

If , the family of straight lines is either concurrent at

If are in H.P. then the straight line  passes through a point, that point is

Consider a family of straight lines . The equation of the straight line belonging to this family that is the farthest form is

The circle $\mathrm{x}^2+\mathrm{y}^2+2 \lambda \mathrm{y}=0, \lambda \in \mathrm{R}$, touches the parabola $\mathrm{x}^2=4 \mathrm{y}$ externally. Then

A light ray emerging from the point source placed at $\mathrm{P}(2,3)$ is reflected at a point ${ }^{\prime} \mathrm{Q}^{\prime}$ on the y-axis and then passes through the point $\mathrm{R}(5,10)$. Coordinate of ' $\mathrm{Q}^{\prime}$ is -

Find the line passing through $(9,-1)$ and the point of intersection of lines $7 x$ $y+1=0$ and $3 x-2 y+7=0$