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A circle has the equation x^2 + y^2 - 4x + 10y - 115 = 0. Express the equation in the form (x - a)^2 + (y - b)^2 = k, and find the centre and radius of the circle.

Rearrange the equation so that the x terms and y terms bracketed together, like so: (x^2 - 4x) + (y^2 + 10y) - 115 = 0. Complete the square on both sets of brackets, giving (x - 2)^2 - 4 + (y + 5)^2 - 25 - 1...
JB
Answered by Joseph B. • Maths tutor
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Find the indefinite integral of ( 32/(x^3) + bx) over x for some constant b.

To integrate (32/ x 3 + bx) over x we can integrate each part separately. This is because addition of two integrals is the same as integrating the total of the elements. So we integrate 32/x 3 first, see tha...
BO
Answered by Becky O. • Maths tutor
3658 Views

Find the set of values of k for which x^2 + 2x+11 = k(2x-1)

The discriminant for a quadratic polynomial of the form f(x) = ax^2 + bx + c is given by b^2 - 4ac. If the discriminant is strictly greater than 2, the quadratic has 2 real distinct roots, i.e 2 unique x-val...
WA
Answered by William A. • Maths tutor
14464 Views

Parlami di cosa hai fatto durante le vacanze di Natale.

Le mie vacanze di Natale non sono state particolarmente emozionanti. Alla mia famiglia piace rispettare le tradizioni, quindi ho passato la vigilia coi miei nonni paterni e il giorno di natale con la nonna m...
LV
Answered by Lorenzo V. • Maths tutor
10648 Views

The line y=5-x intersects the curve y=x^2-3x+2 at the points P and Q. Find the (x,y) coordinates of P and Q.

Step 1: To find the points of intersection, we must find where the y and x values are equal. Therefore 5-x=x 2 -3x+2 where the y-values are equal. Step 2: Rearrange the above into the quadratic equation x 2 ...
GB
Answered by Georgina B. • Maths tutor
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