Parabolas, Ellipses, and Hyperbolas (AQA A-Level Further Maths): Quizzes

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Parabolas, Ellipses, and Hyperbolas
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What curve forms when a plane intersects a cone parallel to its curved face?

Parabola

What is the standard form equation for a parabola with vertex at the origin opening right?

y2=kxy^2 = kx

For ellipse x2a2+y2b2=1\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, which points does it pass through?

(±a,0)(\pm a, 0) and (0,±b)(0, \pm b)

When does the ellipse x2a2+y2b2=1\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 become a circle?

When a=ba = b

For hyperbola x2a2−y2b2=1\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1, which axis does it NOT cross?

yy-axis

What are the asymptotes of hyperbola x2a2−y2b2=1\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1?

y=±baxy = \pm \frac{b}{a}x

What are the asymptotes of rectangular hyperbola xy=c2xy = c^2?

x=0x = 0 and y=0y = 0

What is the vertex of parabola (y−3)2=4a(x+2)(y - 3)^2 = 4a(x + 2)?

(−2,3)(-2, 3)

Where is the centre of ellipse (x−5)29+(y+2)24=1\frac{(x - 5)^2}{9} + \frac{(y + 2)^2}{4} = 1?

(5,−2)(5, -2)

How do you reflect a curve in the line y=xy = x?

Swap xx and yy in equation

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