CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Power of a Point

Let x y be ...

Question

Let x & y be the real numbers satisfying the equation $x^{2} - 4 x + y^{2} + 3 = 0$ .If the maximum and minimum values of $x^{2} + y^{2}$ are M & m respectively , then find the numerical value of (M+m).

Open in App

Solution

$x^{2} - 4 x + y^{2} + 3 = 0$

$\Rightarrow x^{2} - 4 x + 4 + y^{2} - 1 = 0$

${(x - 2)}^{2} + y^{2} = 1$

represents a circle with center at $(2, 0)$ $&$ radius $= 1$ units

$∴ x^{2} + y^{2} \leq 3$

$x^{2} + y^{2} \geq 1$

$∴ M = 3, m = 1$

$∴ M + m = 4$

Hence, the answer is $4.$

Suggest Corrections

thumbs-up

0

Similar questions

Q. If x and y are non zero real numbers satisfying

x y (x^{2} - y^{2}) = x^{2} + y^{2}

, find the minimum value of

x^{2} + y^{2}

Q. In the equation

x^{2} + y^{2} - 4 x + 3 = 0

is satisfied for real values of

x

y

x

y

be real numbers satisfying the inequality

5 x^{2} + y^{2} - 4 x y + 24 \leq 10 x - 1.

Find the value of

x^{2} + y^{2} - 29.

(correct answer + 2, wrong answer 0)

f (x) = | x^{2} - 4 x + 3 |

be a function defined on

x \in [0, 4]

α, β, γ

are the abscissas of the critical points of

f (x) .

m

M

are the local and absolute maximum values of

f (x)

respectively, then the value of

α^{2} + β^{2} + γ^{2} + m^{2} + M^{2}

x, y, z

are real numbers such that

x + y + z = 4

x^{2} + y^{2} + z^{2} = 6

, then the number of integral value(s) of

x

satisfying the equation is

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Power of a Point

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon