the straight line 3x+4y=20 and the circle x^2+y^2-6x-8x=0 at A and B then the equation of the circle of which AB is a diameter is
Answers
Answer:
Consider the circle x
2
+y
2
−6x+4y=12. Then one of the equations of a tangent to this circle that is parallel to the line 4x+3y+5=0 is :
Step-by-step explanation:
Answer
x
2
+y
2
−6x+4y−12=0
=> (x−3)
2
+(y+2)
2
=5
2
This is a circle whose centre is (3,−2) and radius 5
Any line parellel to 4x+3y+5=0 can be written in form 4x+3y+c=0 (as the slope of both lines is same)
Therefore, let the tangent to the circle be 4x+3y+c=0
Now, we need to find out value of c for which this line is tangent to the given circle. We know that lenght of tangent from the centre of the circle is equal to it's radius.
=> perpendicular distance of 4x+3y+c=0 from (3,−2) should be equal to 5
Applying the formulae for perpendicular distance of a point from a line, we get
4
2
+3
2
∣4(3)+3(−2)+c∣
=5
=> ∣6+c∣=25
=>6+c=25;6+c=−25
=> c=19,−31
Therefore, equation of tangents are 4x+3y+19=0;4x+3y−31=0