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The point P, (-1,4) lies on a circle C that is centered about the origin. Find the equation of the tangent to the circle at point P.

The most important fact to remember with this question is that two perpendicular straight lines have gradients related by m 1 = -1/m 2. This can then be used to find the gradient of the tangent by first find...
JA
Answered by James A. • Maths tutor
5092 Views

Solve "x^2 - 12x - 45 = 0" by completing the square

The equation is of the formx 2 +bx+c=0This means it can be rearranged to(x+(b/2)) 2 =(b/2) 2 -cTaking the square root of both sides leaves us with x. x 2 -12x-45=0(x-(12/2)) 2 -(12/2) 2 -45 = 0(x-6) 2 -6 2 -...
EJ
Answered by Elsa J. • Maths tutor
7059 Views

Consider f(x)=x/(x^2+1). Find the derivative f'(x)

To answer this question we need to decide which differentiation rule to use . The quotient rule looks like the obvious choice, so lets try that. If f(x)=u(x)/v(x) (being careful that v(x) is not zero anywher...
JH
Answered by Jack H. • Maths tutor
4807 Views

How do I find the roots of a quadratic equation?

A quadratic equation is one that contains an x^2 term that has a non 0 coefficient, There are three basic methods for solving a quadratic equation; factorising, completing the square, and the quadratic formu...
MC
Answered by MacGregor C. • Maths tutor
4689 Views

Express 8/((root3) -1)) in the form a(root3) +b, where a and b are integers.

You would multiply both numerator and denominator by the expression (root3 +1)/(root3 +1). This expression is equal to 1 hence the original expression remains unchanged. The new expression is now (8(root3)+8...
SK
Answered by Shubham K. • Maths tutor
7366 Views