SOLUTION: what is the equation of the line tangent to the circle x^2+y^2=25 at the point (3,4) ?
I don't know how to go about this sum. Please solve and explain
thanks
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Question 237326: what is the equation of the line tangent to the circle x^2+y^2=25 at the point (3,4) ?
I don't know how to go about this sum. Please solve and explain
thanks
Found 2 solutions by solver91311, eggsarecool:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The general equation of a circle with center at )
and radius 
is
^2 + (y - k)^2 = r^2)
Hence the circle
Must be centered at the origin.
The line tangent to the point )
is perpendicular to the radius segment with endpoints )
and
Determine an equation of the line that contains the aforementioned radius segment by using the two point form of the equation of a line:
(x - x_1) )
Where )
and )
are the coordinates of the given points.
Solve the resulting equation for 
to put this equation into slope-intercept form. Then determine the slope of the radius segment by inspection of the coefficient on 
.
Next use the fact that the slopes of two perpendicular lines are negative reciprocals, that is:
Calculate the negative reciprocal of the slope of the radius segment to get the slope of the tangent.
Then use the point-slope form of the equation of a line with the calculated slope and the point to derive the desired equation:
 )
Where 
is the calculated slope and is the point
John
Answer by eggsarecool(46) (Show Source): You can put this solution on YOUR website!
You need to implicit differentiation for this problem and solve for
So we have.
The derivative is the 2y produces the because y is a function so you have to apply the chain rule to it.
So now.
And x and y are given by (3,4) giving x=3 and y=4. (,)
So
Now for the tangent line you have.
so we have
Giving us Add 4 to both sides. 4 can be rewritten as
And that is your tangent line.
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