## Part - 1

MISCELLANEOUS EXERCISE |

**Question 24. **A person standing at the junction (crossing) of two straight paths represented by the equations 2*x* – 3*y* + 4 = 0 and 3*x* + 4*y* – 5 = 0 wants to reach the path whose equation is 6*x* – 7*y* + 8 = 0 in the least time. Find equation of the path that he should follow.

**Question 23. **Prove that the product of the lengths of the perpendiculars drawn from the points (\sqrt{a^2-b^2}, 0) and (-\sqrt{a^2-b^2}, 0) to the line \frac{x}{a} \cos \theta + \frac{y}{b} \sin \theta = 1 is b^2 .

## Part - 2

**Question 22. **A ray of light passing through the point (1, 2) reflects on the *x*-axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A.

**Question 21. **Find equation of the line which is equidistant from parallel lines 9*x* + 6*y* – 7 = 0 and 3*x* + 2*y* + 6 = 0.

**Question 20. **If sum of the perpendicular distances of a variable point P (*x*, *y*) from the lines *x* + *y* – 5 = 0 and 3*x* – 2*y* +7 = 0 is always 10. Show that P must move on a line.