Question 0115

Equations and Inequalities

2015 Paper 1 Question 1 Variant

Question

A curve

{C}

has equation

\displaystyle y = \frac{a}{x^2} + bx + c,

where

{a,b}

and

{c}

are constants. It is given that

{C}

passes through the points with coordinates

{(1.6, -7.2 )}

and

{(-0.7, -3.7 ),}

and that the gradient of

{C}

is

{3}

where

{x=1.}

(i)

Find the values of

{a,b}

and

{c,}

giving yours answers correct to 3 decimal places.

[4]

(ii)

Find the

{x\textrm{-coordinate}}

of the point where

{C}

crosses the

{x\textrm{-axis},}

giving your answer correct to 3 decimal places.

[2]

(iii)

One asymptote of

{C}

is the line with equation

{x=0.}

Write down the equation of the other asymptote of

{C.}

[1]

Answer

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