Conic sectionsAQA A-Level Further Maths: Flashcards

What these 13 flashcards ask

Shape and symmetry of y^2=4ax?
Vertex of y^2=4ax?
Value of a for y^2=12x?
Equation of an ellipse centred at the origin?
Intercepts of \frac{x^2}{a^2}+\frac{y^2}{b^2}=1?
When is an ellipse a circle?
Equation of the hyperbola with x-intercepts \pm a?
Does \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 meet the y-axis?
Asymptotes of \frac{x^2}{a^2}-\frac{y^2}{b^2}=1?
Quick method for the asymptotes of a hyperbola?
Asymptotes of xy=c^2?
In which quadrants is xy=c^2 (with c\ne0)?
How do you find where a conic meets a line?

Exam questions on Conic sections

An ellipse $E$ has equation $\dfrac{x^2}{25}+\dfrac{y^2}{9}=1$ .
The line $y=\frac95$ meets $E$ at two points. Find the distance between them.2 marks
A parabola $P$ has equation $y^2=12x$ .
Find the coordinates of the points where $P$ meets the line $y=2x$ .2 marks
A hyperbola $H$ has equation $\dfrac{x^2}{16}-\dfrac{y^2}{9}=1$ .
Write down the coordinates of the points where $H$ meets the $x$ -axis, and show that $H$ does not meet the $y$ -axis.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).