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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 ...

Answered by Tilly C. • Maths tutor

4492 Views

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

i...

Answered by Oscar S. • Maths tutor

3978 Views

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 x³ becomes 3x², -3x² becomes -6x, and -9x (which can be written as -9x¹ ) becomes -9. ...

Answered by Tutor105800 D. • Maths tutor

9320 Views

A semicircle has a diameter of 8cm, what it the area?

Area of a circle = pi × r²

Area of semi-circle = 1/2(Area of circle)

= 1/2(pi × r²)

Diameter = 2r

r = 8÷2 = 4

Area of semi-circle = 1/2(pi × 4

Answered by Annabelle P. • Maths tutor

7631 Views

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 ...

Answered by Nicholas H. • Maths tutor

5055 Views