Statement-1: There is one line through A(4, - | vedclass

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Question

(B) First,calculate the distance $AB$ between points $A(4, -5)$ and $B(-2, 3)$ using the distance formula: $AB = \sqrt{(-2 - 4)^2 + (3 - (-5))^2} = \s

Vedclass · Accepted Answer

Statement-$1$ is false,Statement-$2$ is true.

Vedclass · Answer

(B) First,calculate the distance $AB$ between points $A(4, -5)$ and $B(-2, 3)$ using the distance formula: $AB = \sqrt{(-2 - 4)^2 + (3 - (-5))^2} = \sqrt{(-6)^2 + (8)^2} = \sqrt{36 + 64} = \sqrt{100} = 10$. Thus,Statement-$2$ is true.For Statement-$1$,consider a line passing through $A$ with distance $d = 12$ from point $B$. Since the distance $d = 12$ is greater than the distance $AB = 10$,such a line exists. Specifically,there are two such lines (tangents to the circle centered at $B$ with radius $12$ passing through $A$). Since the question states there is 'one' line,Statement-$1$ is false because there are actually two such lines. Therefore,Statement-$1$ is false and Statement-$2$ is true.

Statement-$1$: There is one line through $A(4, -5)$ such that its distance from $B(-2, 3)$ is $12$.
Statement-$2$: $AB = 10$.

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Statement-$1$: There is one line through $A(4, -5)$ such that its distance from $B(-2, 3)$ is $12$.Statement-$2$: $AB = 10$.