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(a)(i) Consider is a circle with centre Origin and radius . Thus, required area is the area of a quadrant with radius (ii) (b) Back to June Revision Exercise 3

(i) When Hence

(a) (b) Back to June Revision Exercise 3

(i) (ii) Area of R As Back to June Revision Exercise 3

(a)(i) Let (a)(ii) *Students are expected to prove that gives the maximum area. (b)(i) latex xlatex \Rightarrow \frac{dy}{dx}=0latex y=-x^2latex y=-x^2latex x^3 + 2y^3 +3xy=klatex x^3 + 2(-x^2)^3 [...]

(i) When Equation of tangent: Equation of normal: (ii) Hence, tangent cuts curve again at (iii) At Q, At R, Back to June Revision Exercise 3

(i) For tangents to be parallel to the -axis, Sub into Thus, equations of tangents which are parallel to -axis are (ii) units per second. Back to June Revision Exercise 3

Please do check through the solutions on your own, especially for questions that we did not have chance to properly discuss during class. You may whatsapp me too if you have a burning question. [...]

(i) If they intersect, then for some Solving with GC, we have . Thus, the lines intersect. (ii) Equation of plane: (iii) Required distance (iv) Area of quadrilateral Back to June Revision Exercise 8.

(a) (b) If the plane contains the line , the is parallel to : and the point lies in the plane : Alternatively, you may consider that : — (1) — (2) Solving, Back to June Revision Exercise 8.