Tangents and normals to the parabola and rectangular hyperbola Quiz

1. Find the gradient of the tangent to $y^2=4x$ at $(4,4)$, using $y=2x^{1/2}$.

• A. $2$
• B. $\frac14$
• C. $\frac12$
• D. $1$

2. Find the gradient of the tangent to $xy=18$ at the point $(3,6)$.

• A. $-2$
• B. $-6$
• C. $2$
• D. $-\frac12$

3. The tangent to a curve at a point has gradient $-\frac34$. What is the gradient of the normal there?

• A. $\frac34$
• B. $-\frac43$
• C. $\frac43$
• D. $-\frac34$

4. Find the equation of the tangent to $xy=12$ at $(2,6)$.

• A. $y=-3x+12$
• B. $y=3x$
• C. $y=-6x+18$
• D. $y=-\frac13x+\frac{20}{3}$

5. Find the equation of the normal to $y^2=4x$ at $(4,4)$ (gradient of tangent $\frac12$).

• A. $y=\frac12x+2$
• B. $y=-2x+12$
• C. $y=2x-4$
• D. $y=-\frac12x+6$