Thread: Problem in Coordinate geometry

I’ve two question please help me to solve.

1. The line y = 0 is a tangent to the circle (x - 8)^2 + (y - a)^2 = 16. Find the value of a.

2. The circle, center (p, q) radius 25, meets the x-axis at (-7, 0) and (7, 0), where q > 0.
a) Find the value of p and q.
b) Find the coordinates of the points where the circle meets the y-axis.

Originally Posted by geton

I’ve two question please help me to solve.

1. The line y = 0 is a tangent to the circle (x - 8)^2 + (y - a)^2 = 16. Find the value of a.

2. The circle, center (p, q) radius 25, meets the x-axis at (-7, 0) and (7, 0), where q > 0.
a) Find the value of p and q.
b) Find the coordinates of the points where the circle meets the y-axis.

1. The distance of the centre of the circle to the x-axis (y = 0) has to equal the radius. (Why?) Therefore ......

2. (a) By symmetry, p = 0 (draw a rough sketch to see why). Then x^2 + (y - q)^2 = 25^2. Now sub either of (-7, 0) or (7, 0) and solve for q.

(b) (0, q + 25) and (0, q - 25) (why?)

Originally Posted by mr fantastic

1. The distance of the centre of the circle to the x-axis (y = 0) has to equal the radius. (Why?) Therefore ......

2. (a) By symmetry, p = 0 (draw a rough sketch to see why). Then x^2 + (y - q)^2 = 25^2. Now sub either of (-7, 0) or (7, 0) and solve for q.

(b) (0, q + 25) and (0, q - 25) (why?)

By this way,
1. I found a^2 = - 48. But answer is a = 4.
2. a. q^2 = - 24. But answer is q = 24.



I'm totally confused.

Originally Posted by geton

By this way,
1. I found a^2 = - 48. But answer is a = 4. Mr F says: Remind me - what did I say about the distance of the centre from the x-axis? Hmmmm ..... And the radius is 4 .... Hmmmmm ......

2. a. q^2 = - 24. But answer is q = 24. Mr F says: x^2 + (y - q)^2 = 25^2. I'll sub (7, 0) and solve for q: (7)^2 + (-q)^2 = 25^2 => 49 + q^2 = 25^2 => q^2 = 25^2 - 49 = (25 - 7)(25 + 7) = (18)(32) therefore . Or you could have recognised and exploited the pythagorean triple (7, 24, 25). Why use a calculator when you can exercise your brain.



I'm totally confused.

Without seeing any of your working it's difficult to know which of the many potential mistakes you might have made. Tip for the future: Show your working, not just your answers.