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could anyone help me with this circle question

a circle c has equation (x-5)^2 (y 3)^2=10, the line l is a tangent to the circle and has gradient -3. Find the 2 possible equations for l in the form y=mx c
Original post by mikeft
a circle c has equation (x-5)^2 (y 3)^2=10, the line l is a tangent to the circle and has gradient -3. Find the 2 possible equations for l in the form y=mx c

Ignoring the missing (plus?) signs, what have you tried / what are you stuck with?
(edited 1 year ago)
Original post by mikeft
a circle c has equation (x-5)^2 (y 3)^2=10, the line l is a tangent to the circle and has gradient -3. Find the 2 possible equations for l in the form y=mx c

There's a typo in your equation....

What have you tried? Could you use the fact that the radius of the circle is perpendicular to the tangent to make some progress?
(edited 1 year ago)
Reply 3
Original post by mqb2766
Ignoring the missing (plus?) signs, what have you tried / what are you stuck with?

for the first equation I know the gradient is -3 but I am confused on how to find the point
also it asks about 2 equations how would I find the second equation
Original post by mikeft
for the first equation I know the gradient is -3 but I am confused on how to find the point
also it asks about 2 equations how would I find the second equation

You have the equation of the circle and you know the gradient of the line (tangent). So the two (line) equations its referring to are the two corresponding values for "c", so the two lines which have that gradient and are tangent to the circle (at different points). The usual ways to proceed are using simultaneous equations / discriminant or geometry, as above.

If youve not sketched it (circle, tangents), it may help to make it clearer.
(edited 1 year ago)
Reply 5
Original post by mqb2766
You have the equation of the circle and you know the gradient of the line (tangent). So the two (line) equations its referring to are the two corresponding values for "c", so the two lines which have that gradient and are tangent to the circle (at different points). The usual ways to proceed are using simultaneous equations / discriminant or geometry, as above.

If youve not sketched it (circle, tangents), it may help to make it clearer.

I am a bit confused how will I use the equation of the circle if the lines do not pass threw the centre
Original post by mikeft
I am a bit confused how will I use the equation of the circle if the lines do not pass threw the centre

Have you drawn a sketch, if so, upload it.

You must have an example in your textbook which goes through the simultaneous equation / discriminant method, or find the points on the circle which represent the tangent points as previously suggested.
(edited 1 year ago)
Reply 7
Original post by mqb2766
Have you drawn a sketch, if so, upload it.

You must have an example in your textbook which goes through the simultaneous equation / discriminant method, or find the points on the circle which represent the tangent points as previously suggested.

I am going to look in my textbook because I am still really confused
Original post by mikeft
I am going to look in my textbook because I am still really confused

Its a fairly standard circle / tangent question, so if you've not looked in your textbook for an example, you should certainly do so. As above, the usual way to solve it is simultaneous (quadratic) equations and discriminant, as there is only a single intersection point for each tangent line (not two or zero). However, most such problems can also be solved with geometry as well. Neither should be that hard.
(edited 1 year ago)

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