Assertion (A): The point on the x-axis which is equidistant from (2,-5)and

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Q.
Assertion (A): The point on the x-axis which is equidistant from (2,-5) and (-2,9) is (8,0).

Reason (R): Points lying on the y-axis are always of the form (0,y).

1 Both A and R are true, and R is the correct explanation of A.

2 Both A and R are true, but R is not the correct explanation of A.

3 A is true, but R is false.

4 A is false, but R is true

Ans.
(4)

$P A = P B \Rightarrow \sqrt{(x - 2)^{2} + (0 + 5)^{2}} = \sqrt{(x + 2)^{2} + (0 - 9)^{2}}$

$S q u a r i n g b o t h s i d e s : (x - 2)^{2} + 25 = (x + 2)^{2} + 81$

$x^{2} - 4 x + 4 + 25 = x^{2} + 4 x + 4 + 81$

$- 8 x = 56 \Rightarrow x = \frac{56}{- 8} = - 7$

$T h u s, t h e p o i n t o n x - a x i s i s (- 7, 0), n o t (8, 0)$

$S o : A s s e r t i o n (A) i s f a l s e b u t R e a s o n (R) i s t r u e$

Solution

Q.
Assertion (A): The point on the x-axis which is equidistant from (2,-5) and (-2,9) is (8,0).

Reason (R): Points lying on the y-axis are always of the form (0,y).

1 Both A and R are true, and R is the correct explanation of A.

2 Both A and R are true, but R is not the correct explanation of A.

3 A is true, but R is false.

4 A is false, but R is true

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Solution

Q. Assertion (A): The point on the x-axis which is equidistant from (2,-5) and (-2,9) is (8,0). Reason (R): Points lying on the y-axis are always of the form (0,y).

1 Both A and R are true, and R is the correct explanation of A.

2 Both A and R are true, but R is not the correct explanation of A.

3 A is true, but R is false.

4 A is false, but R is true

Ans. (4) PA=PB⇒(x-2)2+(0+5)2=(x+2)2+(0-9)2 Squaring both sides:(x-2)2+25=(x+2)2+81 x2-4x+4+25=x2+4x+4+81 -8x=56⇒x=56-8=-7 Thus, the point on x-axis is (-7,0), not (8,0) So: Assertion (A) is false but Reason (R) is true

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Q.
Assertion (A): The point on the x-axis which is equidistant from (2,-5) and (-2,9) is (8,0).

Reason (R): Points lying on the y-axis are always of the form (0,y).