Question

the equation of tangent to the circle X2+y2=25 at (-3,4) is​

Answer 1

The answer is:

y

=

3

4

x

+

25

4

.

The circle is not a function, so we have to divide it in two half.

y

=

±

√

25

−

x

2

.

We need the above semicircle, because the point is in the second quadrant. So the function we need is:

y

=

+

√

25

−

x

2

.

Its derivative is:

y

'

=

1

2

√

25

−

x

2

⋅

(

−

2

x

)

=

−

x

√

25

−

x

2

.

The slope in the point

(

−

3

,

4

)

is:

y

'

(

−

3

)

=

−

−

3

√

25

−

9

=

3

4

.

So the tangent line is:

y

−

4

=

3

4

(

x

+

3

)

⇒

y

=

3

4

x

+

25

4

.