“One Of The Lessons That I Grew Up With Was To Always Stay True To Yourself And Never Let What Somebody Else Says Distract You From Your Goals.” – Michelle Obama

MISCELLANEOUS EXERCISE |

**Question 4. **An arch is in the form of a semi-ellipse. It is 8 m wide and 2 m high at the center. Find the height of the arch at a point 1.5 m from one end.

**Question 5.** A rod of length 12 cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with the *x*-axis.

**Question 6. **Find the area of the triangle formed by the lines joining the vertex of the parabola \( x^2=12y \) to the ends of its latus rectum.

**Question 7. **A man running a racecourse notes that the sum of the distances from the two flag posts from him is always 10 m and the distance between the flag posts is 8 m. Find the equation of the posts traced by the man.

**Question 8.** An equilateral triangle is inscribed in the parabola \(y^2=4ax\), where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.