Question

6. D’Andre said that a circle with equation (x−2)^2+(y−7)^2=13 has a tangent line represented by the equation y−5=−3/2(x+1). Is he correct? Explain.

Answer 1

Yes, D’Andre is correct.

Explanation:

Please find the attachment.

We have been given a statement. D’Andre said that a circle with equation
`(x-2)^2+(y-7)^2=13` has a tangent line represented by the equation
`y-5=-(3)/(2)(x+1)`. We are asked to determine whether D'Andre is correct or not.

Upon graphing our circle and tangent line, we will get our required graph as shown in the attachment.

Upon looking at the graph, we can see that the equation
`y-5=-(3)/(2)(x+1)` touches the given circle exactly at one point that is
`(-1,5)`.

Therefore, D'Andre is correct.