State whether following statements are true or falseStatement-1 - The only circle having radius -10 and a diameter along line 2x - y-5 is x2 - y2 - 6x - 2y-0-Statement-2- The line 2x - y-5 is a normal to the circle x2- y2 - 6x - 2y -0-

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Definition of Circle

State whether...

Question

State whether following statements are true or false
Statement-1 : The only circle having radius $\sqrt{10}$ and a diameter along line $2 x + y = 5$ is $x^{2} + y^{2} - 6 x + 2 y = 0$ .
Statement-2: The line 2x + y=5 is a normal to the circle $x^{2} + y^{2} - 6 x + 2 y = 0.$

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

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Statement-1 is true,statement-2 is true and statement-2 is NOT the correct explanation for statement-1.

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

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Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.

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Solution

The correct option is A Statement- 1 is false, statement-2 is true.
Statement 1 and 2 both are correct, but statement 2 is not correct explaination for statement 1.

$x^{2} + y^{2} - 6 x + 2 y = 0$

$(- g, - f) = (- 3, 1), c = 0$

$r^{2} = g^{2} + f^{2} - c$

$∴ r^{2} = 9 + 1 - 0 = 10$

$\Rightarrow r = \sqrt{10}$

$2 x + y = 5$ is also a normal to the circle.

Suggest Corrections

Similar questions

Statement 1: If a line $L = 0$ is tangent to the circle $S = 0$ , then it will also be a tangent to the circle $S + λ L = 0$

Statement 2: If a line touches a circle, then perpendicular distance of the line from the centre of the circle is equal to the radius of the circle.

Q. Statement

- 1 :

x^{{log}_{x} (3 - x)^{2}} = 25

, then

x = - 2

Statement

- 2 :

a^{{log}_{a} x} = x

, if

a > 0, x > 0

and

a \neq 1

Q. Lines

L_{1} : y - x = 0

and

L_{2} : 2 x + y = 0

intersect the line

L_{3} : y + 2 = 0

P

and

Q

, respectively. The bisector of the acute angle between

L_{1}

and

L_{2}

intersects

L_{3}

at R.

STATEMENT-1 : The ratio

P R : R Q

equals

2 \sqrt{2} : \sqrt{5} .

because

STATEMENT-2: In any triangle, bisector of an angle divides the triangle into two similar triangles.

Q. Statement

- 1 :

0 < x < y \Rightarrow {log}_{a} x > {log}_{a} y

, where

a > 1

.
Statement

- 2 :

When

a > 1, {log}_{a} x

is an increasing function.

Q. Consider the system of equations

x + y + z = 6,

x + 2 y + 3 z = 10

and

x + 2 y + λ z = μ

Statement

1

: If the system has infinite number of solutions, then

μ = 10.

Statement

2

: The value of

∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 6 1 & 2 & 10 1 & 2 & μ \end{matrix} ∣ ∣ ∣ ∣ = 0 for μ = 10.

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State whether following statements are true or falseStatement-1 : The only circle having radius √10 and a diameter along line 2x+y=5 is x2+y2−6x+2y=0.Statement-2: The line 2x + y=5 is a normal to the circle x2+y2−6x+2y=0.

The correct option is A Statement- 1 is false, statement-2 is true.Statement 1 and 2 both are correct, but statement 2 is not correct explaination for statement 1.x2+y2−6x+2y=0(−g,−f)=(−3,1),c=0r2=g2+f2−c∴r2=9+1−0=10⇒r=√102x+y=5 is also a normal to the circle.

State whether following statements are true or false
Statement-1 : The only circle having radius $\sqrt{10}$ and a diameter along line $2 x + y = 5$ is $x^{2} + y^{2} - 6 x + 2 y = 0$ .
Statement-2: The line 2x + y=5 is a normal to the circle $x^{2} + y^{2} - 6 x + 2 y = 0.$