Write the equation of the circle with center at (-4,\ -5) and to

enfurezca3x

enfurezca3x

Answered question

2021-11-15

Write the equation of the circle with center at (4, 5) and touching the line 3x2y7=0

Answer & Explanation

Ched1950

Ched1950

Beginner2021-11-16Added 21 answers

Step 1
Consider that the center of circle be (4, 5) and line 3x2y7=0 touches the circle.
Since the line 3x2y7=0 touches the circle implies the shortest distance of the centre and line is the radius.
Shortest distance of a line Ax+By+C=0 from the point (a, b) is given by: |Aa+Bb+CA2+B2|
Therefore,
r=|3(4)2(5)732+(2)2|
=|12+1079+4|
=913
Step 2
Equation of circle with center (a, b) and radius r is given by (xa)2+(yb)2=r2
Since centre is (4, 5) and radius is 913. Therefore, equation of circle become:
(x(4))2+(y(5))2=(913)2
(x+4)2+(y+5)2=8113

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