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How do you find the point or points of intersection of a straight line and a circle?

Given the equation of the straight line is: x+y=9 and the equation of the circle is: (x-2) 2 +(y-3) 2 =16 , find the point or points of intersection? The equation x+y=9 can be rearranged to make x=9-y. This ...
EC
Answered by Edward C. • Maths tutor
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How do I answer source-based questions?

Paper 1 is a source-based paper split into four questions. Each question requires a different technique in order to gain top marks. Question 1 is split into two parts, both parts are testing your basic under...
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Answered by Bethany E. • History tutor
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'Considering an abortion is a question of choice, not a question of life.' Discuss.

This question raises a number of issues: whether women have complete freedom over their body's or not; at what point does a foetus become a person; should a foetus with a disability be treated differently; w...
AL
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It is given that f(x) = 2sinhx+3coshx. Show that the curve y = f(x) has a stationary point at x =-½ ln(5) and find the value of y at this point. Solve the equation f(x) = 5, giving your answers exactly

1.Differentiating: f'(x)= 2cosh(x)+3sinh(x) At a stationary point, we know f'(x)=0. Therefore 2cosh(x)+3sinh(x)=0. (easy to forget that unlike nromal trig there is no change in sign) Rearranging gives tanh(x...
SB
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Integrate | x^7 (ln x)^2 dx ( | used in place of sigma throughout question)

Start the integration by parts process |udv = uv - |vdu u = (ln x) 2 dv = x 7 dx du = 2(ln x)/x dx v = 1/8 x 8 = 1/8 x 8 (ln x) 2 - | 1/4(ln x)x 7 dx = 1/8 x 8 (ln x) 2 -1/4 | x 7 (ln x) dx Repeat the integr...
RD
Answered by Rowan D. • Maths tutor
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