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The chord of contact of (2,1) with respe...

The chord of contact of (2,1) with respect to the circle `x^(2)+y^(2)=2` is

A

`x+2y=2`

B

`2x+y=2`

C

`2x+y=1`

D

`x+2y=sqrt(2)`

Text Solution

AI Generated Solution

The correct Answer is:
To find the chord of contact of the point (2, 1) with respect to the circle given by the equation \(x^2 + y^2 = 2\), we can follow these steps: ### Step 1: Identify the Circle and Point The equation of the circle is given as: \[ x^2 + y^2 = 2 \] We have a point \(P(2, 1)\) from which we want to find the chord of contact. ### Step 2: Write the General Equation of the Circle We can rewrite the equation of the circle in the form: \[ x^2 + y^2 - 2 = 0 \] Here, we can identify \(c = 2\). ### Step 3: Use the Formula for the Chord of Contact The chord of contact from a point \((x_1, y_1)\) to the circle \(x^2 + y^2 = r^2\) is given by: \[ xx_1 + yy_1 = r^2 \] For our case, \(x_1 = 2\), \(y_1 = 1\), and \(r^2 = 2\). ### Step 4: Substitute the Values into the Formula Substituting the values into the chord of contact formula: \[ xx_1 + yy_1 = r^2 \] we get: \[ x(2) + y(1) = 2 \] This simplifies to: \[ 2x + y = 2 \] ### Step 5: Rearranging the Equation We can rearrange the equation to standard form: \[ 2x + y - 2 = 0 \] ### Conclusion Thus, the chord of contact of the point (2, 1) with respect to the circle \(x^2 + y^2 = 2\) is: \[ 2x + y = 2 \]
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