*“Try not to become a person of success, but rather try to become a person of value.” –Albert Einstein*

# Lecture - 12 Chapter 10 Straight Lines

NCERT EXERCISE 10.3 |

**Question 14.Â **Find the coordinates of the foot of perpendicular from the point (â€“1, 3) to the line 3*x* â€“ 4*y* â€“ 16 = 0.

**Question 15.Â **The perpendicular from the origin to the line *y* = *mx* + *c* meets it at the point (â€“1, 2). Find the values of *m* and *c*.

**Question 16. **If *p* and *q* are the lengths of perpendiculars from the origin to the lines \( x \cos \theta – y \sin \theta = k \cos 2 \theta \) and \( x \sec \theta + y \cosec \theta = k\), respectively, prove that \( p^2+4q^2=k^2 \).

**Question 17.Â **In the triangle ABC with vertices A (2, 3), B (4, â€“1) and C (1, 2), find the equation and length of altitude from the vertex A

**Question 18.Â **If *p* is the length of perpendicular from the origin to the line whose intercepts on the axes are *a* and *b*, then show that \( \frac{1}{p^2}= \frac{1}{a^2}+\frac{1}{b^2} \).