*“Great minds discuss ideas; average minds discuss events; small minds discuss people.” –Eleanor Roosevelt*

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* – 7*y* + 5 = 0 and 3*x* + *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).