Coordiante geometry in the (x, y) plane?

Question

find the tangent to the circle (x+4)^2 + (y-1)^2 = 242 at (7, 10) meets the y axis at S and the x axis at T.

a) find the coordinate's of S and T.
b) hence, find the aera of triangle OST, where O is the Origin.

havent done mathematics in a while (I am not a High School , College or University student), so I was referring to my old A-Leverl books and I was trying out sums and this one's quite hard for me so if you can then show me how to tackle this sum if possible then step by step.

thank you very much.

Anonymous · Accepted Answer

The tangent to a circle is always perpendicular to the radius at that point. Using this knowledge, you would calculate the circle's centre coordinates, and use these and the point on the outer edge you're given to work out the gradient of the radius.

The centre of the circle is, when you have the equation in the form of (x - a)^2 + (y - b)^2 = r^2, at point [a, b]. So in this case, your centre is at [-4, 1]. The other point on the outer edge of the circle is at [7, -10], so the gradient of the radius is:

(1 - -10) / (-4 - 7) = 11/-11 = -1

The gradient of the line perpendicular to this is always the negative reciprocal of this gradient, which will give you a gradient of 1.

With this gradient, and the point you're given, you have everything you need to know to calculate the equation of the tangent line, which will give you every bit of information you need to answer the two questions.

Hope this at least gets you on your way.

Dan A · Answer

You sure you didnt mean to write (7,12) rather than (7,10)? Did you write the equation correctly? The circle doesnt pass through the point (7,10) or (7,-10).

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Coordiante geometry in the (x, y) plane?

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