Maths help!

$Avatar for hiy\a$

The circle C has the equation x^2 - 8x + y^2 + 4y - 29=0
The tangent from the point P(-16,13) touches the circle at point Y
Find the distance PY.
End of Q.

So far I’ve calculated the centre as being (4,-2) and the radius as r=7, but Idk where to go from here...

Reply 1

mqb2766

21

Original post by hiya

The circle C has the equation x^2 - 8x + y^2 + 4y - 29=0
The tangent from the point P(-16,13) touches the circle at point Y
Find the distance PY.
End of Q.

So far I’ve calculated the centre as being (4,-2) and the radius as r=7, but Idk where to go from here...

If you sketch it, the right angled triangle the tangent makes with the centre forms a well known Pythagorean triple which means PY can be written.down .
Alternatively use pythagoras on the right angled triangle PYC. The tangent makes a right angle with the circle radius.

(edited 3 years ago)

Reply 2

$Avatar for hiy\a$

hiy\a

OP

12

Original post by mqb2766

If you sketch it, the right angled triangle the tangent makes with the centre forms a well known Pythagorean triple which means PY can be written.down .
Alternatively use pythagoras on the right angled triangle PYC. The tangent makes a right angle with the circle radius

Ahhh, thank you :smile:

Reply 3

AyyJeh

14

Original post by hiya

The circle C has the equation x^2 - 8x + y^2 + 4y - 29=0
The tangent from the point P(-16,13) touches the circle at point Y
Find the distance PY.
End of Q.

So far I’ve calculated the centre as being (4,-2) and the radius as r=7, but Idk where to go from here...

So you know where P is (-16,13) and you know the centre (4,-2). You also know that a straight line from the centre of the circle to the circumference of the circle is the radius (7). You can find out the length of the line from point P to the centre using basic Pythagoras. Take this line and then the radius and calculate PY using Pythagoras again as the tangent will hit the circle perpendicular and so forms a right angled triangle. (Sketching all of this makes it easier to imagine, just plug in 6/8 or so numbers into the equation and come up with a little circle to help you!

Maths help!

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