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Mathematics
Mathematics
Problem
The length of the chord intercepted by the circle
x
2
+
y
2
=
r
2
x^2 + y^2 = r^2
x
2
+
y
2
=
r
2
on the line
x
a
+
y
b
=
1
\frac{x}{a} + \frac{y}{b} = 1
a
x
+
b
y
=
1
is - (1)
2
r
2
(
a
2
+
b
2
)
−
a
2
b
2
a
2
+
b
2
\frac{2\sqrt{r^2(a^2 + b^2) - a^2b^2}}{a^2 + b^2}
a
2
+
b
2
2
r
2
(
a
2
+
b
2
)
−
a
2
b
2
(2)
2
r
2
(
a
2
+
b
2
)
−
a
2
b
2
a
2
+
b
2
2\sqrt{\frac{r^2(a^2 + b^2) - a^2b^2}{a^2 + b^2}}
2
a
2
+
b
2
r
2
(
a
2
+
b
2
)
−
a
2
b
2
(3)
r
2
(
a
2
+
b
2
)
−
a
2
b
2
a
2
+
b
2
\sqrt{\frac{r^2(a^2 + b^2) - a^2b^2}{a^2 + b^2}}
a
2
+
b
2
r
2
(
a
2
+
b
2
)
−
a
2
b
2
(4) None of these
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