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If the line , where , touches the circle at , find…
MATHEMATICS · Subjective · CBSE · Mathematics · Circles · Circles
Problem
If the line
3
x
−
4
y
+
λ
=
0
3x-4y+\lambda=0
3
x
−
4
y
+
λ
=
0
, where
λ
>
0
\lambda>0
λ
>
0
, touches the circle
x
2
+
y
2
−
4
x
−
8
y
−
5
=
0
x^2+y^2-4x-8y-5=0
x
2
+
y
2
−
4
x
−
8
y
−
5
=
0
at
(
a
,
b
)
(a,b)
(
a
,
b
)
, find
λ
+
a
+
b
\lambda+a+b
λ
+
a
+
b
.
Related theory
Circle (Standard Equation)
Conic Sections
Circles
Tangent to a Circle
Tangent length properties
Tangent theorem (radius perpendicular to tangent)
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