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Find the centre coordinates, and radius of the circle with equation: x^2 + y^2 +6x -8y = 24

Firstly, rearrange the equation to group the 'x' terms together, and the 'y' terms together.x^2 + 6x + y^2 -8y = 24'Complete the square' on each of the x and y groups:(x + 3)^2 - 9 + (y - 4)^2 - 16 = 24Rearr...
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Answered by Sam N. • Maths tutor
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What is Integration

Integration can be conceptually understood in 2 different ways. firstly it is the reverse process of differentiation (Indefinite integration). Secondly it is used to work out the area under a curve (Definite...
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Answered by sulaiman n. • Maths tutor
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Differentiate y = arcsin(x) with respect to x

y = arcsin(x) implies sin(y) = x Differentiating with respect to x gives: cos(y)*dy/dx = 1So: dy/dx = 1/cos(y) Noting that cos(y) = sqrt(1 - sin^2(y)): dy/dx = 1/sqrt(1 - sin^2(y)) = 1/sqrt(1 - x^2)
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Find the coordinates of the centre of the circle with equation: x^2 + y^2 − 2*x + 14*y = 0

method: complete the squares for (x^2 - 2 x ) and ( y^2 + 14 y ) using the formula (b/2)^2 (where the general equation is a x^2 + b x) so that the equation becomes a x^2 + b x + (b/2)^2first, rearrange the o...
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Answered by Catherine A. • Maths tutor
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Prove algebraically that the sum of the squares of two consecutive multiples of 5 is not a multiple of 10.

First let’s break this statement down. At the core of this sentence are two consecutive multiples of 5. How can we represent these using algebra? Let’s use 5a where “a” is an integer. A consecutive multiple ...
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Answered by Daniel S. • Maths tutor
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