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A circle with centre C(2, 3) passes through the point A(-4,-5). (a) Find the equation of the circle in the form (x-a)^2 + (y-b)^2=k

This question is aimed at A-Level Pure Core 1 students. A circle with centre C(2, 3) passes through the point A(-4,-5). Find the equation of the circle in the form (x-a)^2 + (y-b)^2 = k From the formula for ...
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Answered by Tilly C. • Maths tutor
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i) Make y the subject of the expression x = ((a-y)/b))^1/2 ii) Simplify fully (2x^2 − 8)/(4x^2 − 8x)

i) Square both sides of the expression to make x^2=(a-y)/b Multiply by b to remove the fraction from the equation and then rearrange to make y the subject. bx^2=a-y --> y=a-bx^2 ii) First factor out 2 fro...
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Answered by Oscar S. • Maths tutor
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Differentiate x^3 − 3x^2 − 9x. Hence find the x-coordinates of the stationary points on the curve y = x^3 − 3x^2 − 9x

To differentiate, we bring the power down and decrease the power by 1. So x 3 becomes 3x 2 , -3x 2 becomes -6x, and -9x (which can be written as -9x 1 ) becomes -9. So y' = 3x 2 - 6x - 9 This equation tells ...
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Answered by Tutor105800 D. • Maths tutor
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A semicircle has a diameter of 8cm, what it the area?

Area of a circle = pi × r 2 Area of semi-circle = 1/2(Area of circle) = 1/2(pi × r 2 ) Diameter = 2r r = 8÷2 = 4 Area of semi-circle = 1/2(pi × 4 2 )
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Answered by Annabelle P. • Maths tutor
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Evaluate the following integral: (x^4 - x^2 +2)/(x^2(x-1)) dx

This type of question appears over-complicated with limited options, but one must not fear! At first, the numerator seems to be of a higher degree than the denominator (x^4 compared to x^2), but from the fir...
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Answered by Nicholas H. • Maths tutor
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