The equation of a curve is ${{x}^{2}}-bxy+{{y}^{2}}=2b+3$, where $b$ is a constant. Show that the $x

Question

The equation of a curve is ${{x}^{2}}-bxy+{{y}^{2}}=2b+3$, where $b$ is a constant. Show that the $x$-coordinate of any tangents to the curve that are parallel to the $y$-axis satisfy the equation $\left( 4-{{b}^{2}} \right){{x}^{2}}=8b+12$. [4] Determine, algebraically, the set of values of $b$ for the tangents in part (i) to exist. [3]

Accepted Answer

(ii) $b<-2$ 	ext{ or } $-1.5\le b<2$

2018 MI P1 Q7

2018 MI P1 Q7

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