# Lecture-13

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 NCERT EXERCISE 10.3

Question 11. Prove that the line through the point $(x_1, y_1)$ and parallel to the line $Ax+By+C=0$ is $A(x-x_1)+B(y-y_1)=0$

 MISCELLANEOUS EXERCISE

Question 1. Find the values of k for which the line $(k-3)x-(4-k^2)y+k^2-7k+6=0$ is
(a) Parallel to the x-axis
(b) Parallel to the y-axis
(c) Passing through the origin

Question 2. Find the values of $\theta$ and p, if the equation $x \cos \theta + y \sin \theta = p$ is the normal form of the line $\sqrt{3}x+y+2=0$.

Question 3. Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and – 6, respectively.

Question 4. What are the points on the y-axis whose distance from the line $\frac{x}{3}+\frac{y}{4}=1$ is 4 units.

Question 6. Find the equation of the line parallel to y-axis and drawn through the point of intersection of the lines x – 7y + 5 = 0 and 3x + y = 0.

Question 7. Find the equation of a line drawn perpendicular to the line $\frac{x}{4}+\frac{y}{6}=1$ through the point, where it meets the y-axis.

Question 5. Find perpendicular distance from the origin to the line joining the points (cosθ, sin θ) and (cos φ, sin φ).