Tangents and normals to the parabola and rectangular hyperbolaEdexcel International A Level Further Maths: Flashcards

What these 13 flashcards ask

Gradient of the normal in terms of the tangent gradient m?
Equation of a line through (x1,y1) with gradient m?
How do you differentiate the parabola y^2=4ax (for y0) without implicit differentiation?
Gradient of the tangent to y^2=4ax at a point with y-coordinate y?
Gradient of the tangent to xy=c^2 at x?
Rearrangement used before differentiating xy=c^2?
Gradient of the tangent to y^2=12x at (12,12)?
Gradient of the normal to y^2=12x at (12,12)?
Gradient of the tangent to xy=24 at (4,6)?
Equation of the normal to xy=24 at (4,6)?
How do you find where a tangent meets the x-axis?
When a normal meets the curve again, why can you factorise the quadratic easily?
What do the tangent and normal at a point have in common?

Exam questions on Tangents and normals to the parabola and rectangular hyperbola

The parabola $P$ has equation $y^2=12x$ .
Find the equation of the tangent to $P$ at the point $(12,12)$ .2 marks
The rectangular hyperbola $H$ has equation $xy=24$ and passes through the point $A(4,6)$ .
Find the equation of the normal to $H$ at $A$ , in the form $ax+by+c=0$ where $a$ , $b$ and $c$ are integers.2 marks
The parabola $C$ has equation $y^2=8x$ . The point $P$ lies on $C$ , has $x$ -coordinate 8 and has positive $y$ -coordinate.
Find the equation of the tangent to $C$ at $P$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).