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A circle has equation x^2+y^2-8x+10y+41=0. A point on the circle has coordinates (8,-3). Find the equation of the tangent to the circle passing through this point.

From the equation x 2 +y 2 -8x+10y+41=0, we can find the centre of the circle by the middle two terms -8x+10y and multiplying them by -1/2. So the coordinates of the circle centre are (4,-5).Now we can find ...
JK
Answered by Joseph K. • Maths tutor
2651 Views

Find an equation for the straight line AB , giving your answer in the form px+qy=r, where p, q and r are integers. Given that A has co-ordinates (-2,4) and B has co-ordinates (8,-6)

We know 2 equations for a straight line; Y=MX+C and Y-B=M(X-A) . Since we do not have the y intercept (C) or any means of finding it but we do have 2 points on the straight line, it would make sense to use t...
SC
Answered by Samantha C. • Maths tutor
4793 Views

A 25 micro farad is charged until the potential difference across it is 500V. Calculate the charge stored at this moment.

The formula to be used here is C = Q / V. Where C = capacitance, Q = charge and V = potential difference. First we can put in the values to get 25 * 10^-6 = Q / 500. This can be rearranged to Q = 500 * 25 * ...
CW
Answered by Cameron W. • Physics tutor
2780 Views

Differentiate (x-2)^2

Answer is 2x - 4. This is found by following the standard differentiation procedure of n(ax-b)^n-1 where n was the previous power and a and b are the value inside the bracket. This means that it first goes t...
CW
Answered by Cameron W. • Maths tutor
9038 Views

Express '2x^2 + 8x + 30' in the form 'a(x+b)^2 + c'

b = B/2A = 8/(2x2) =8/4 = 2 c = C-((B^2)/4A) = 30-((8^2)/(4x2)) = 30-64/8 = 30-8 = 22 => 2x^2 + 8x + 30 = 2(x+2)^2 + 22
CC
Answered by Charles C. • Maths tutor
4688 Views