What is the equation of the tangent of the circle x^2+y^2=25 at the point (3,4)
GraphFirstly, if not drawn for you it would be best to draw the graph which is given to you (in this case you should notice is a circle with a radius 5 as the general equation for a circle is (x-a)2+(y-b)2=r2 which represents a circle with centre (a,b) and radius r. This will give you a visual representation which should allow you to answer the question easier.
Next, I would recommend adding a sketching of the tangent at the point the question asks for (3,4). This should let you see exactly what you need to find. After it should be possible to notice that if you draw a line between the centre of the circle to the point the tangent touches the circle (3,4).
Your drawing so far should be.
This should remind you of the circle theorem being a radii and tangent meet at a right angle. Meaning the radii and tangent are perpendicular and the gradient of perpendicular lines is the negative reciprocal of the other. The equation of the radius can be round easily as you can just do change in y/change in x from (0,0) and (3,4) giving y=(4/3)x. The negative reciprocal of the gradient is -3/4 giving the equation y=(-3/4)x+c. c can now be found by inputting the values of the point known (3,4) giving 4=(-3/4)*3+c which when rearrange gives 25/4=c. The answer can finally be fully written out as y=(-3/4)x+25/4.
