The diagram shows part of the curve $y = x^2 - 1$, cutting the $x$-axis at $A(1,0)$. The tange

Question

The diagram shows part of the curve $y = x^2 - 1$, cutting the $x$-axis at $A(1,0)$. The tangent at point $B$ on the curve cuts the $x$-axis at $C \left( \frac{5}{4}, 0 \right)$ and $y$-axis at $D(0, -5)$ respectively. The normal at $B$ meets the $x$-axis at $E$. Find the coordinates of $B$.[3] Find the coordinates of $E$.[2] Find the area of the shaded region.[3]

Accepted Answer

(a)(2,3) (b)(14,0) (c)$19\frac{1}{3}$units$^2$

2025 MGS PRELIMS P1 Q12

2025 MGS PRELIMS P1 Q12