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Consider the unit hyperbola, whose equation is given by x^2 - y^2 = 1. We denote the origin, (0, 0) by O. Choose any point P on the curve, and label its reflection in the x axis P'. Show that the line OP and the tangent line to P' meet at a right angle.

We differentiate our equation with respect to x to find that 2x - 2y(dy/dx) = 0, and rearrange to find that dy/dx = x/y. We set P = (x, y). The slope of OP is given by y/x, and the slope of the tangent at...

Answered by Dylan C. • Maths tutor

3187 Views

Show that the volume of the solid formed by the curve y=cos(x/2), as it is rotated 360° around the x-axis between x= π/4 and x=3π/4, is of the form π^2/a. Find the constant a.

After sketching a diagram of the curve and the solid for clarity, we see that we need to use the formula V = π∫ y² dx (with upper and lower bounds of 3π/4 and π/4 respectively) to calculate the...

Answered by Nicholas C. • Maths tutor

3242 Views

Margret wants to share £36 in a ratio of 3:4 between her two grandchildren, Anna and Katie. How much money will Katie get?

36/12 = 33x4 = 12Katie gets £12

Answered by Martha N. • Maths tutor

3823 Views

How can I find the equation of a line l which passes through the points (5,7) and (3, -1)

First thing first, we should always write down the equation of a straight line (which is y = mx + c) as this will be important for this question.In order to find the equation of the strai...

Answered by Katie C. • Maths tutor

9204 Views

Given that x^2+10x+3 can be written in the form (x+a)^2+b, find the values of a and b.

We can tackle this question by completing the square. Completing the square allows us to write a quadratic equation (x^2+10x+3) in the simpler form (x+a)^2+b.To complete the square, first we need to find ...

Answered by Katie C. • Maths tutor

9980 Views