The condition that the straight line joining the origin to the points of intersection of the line $4 x + 3 y = 24$ with the circle $(x - 3)^{2} + (y - 4)^{2} = 25$ .

Are coincident

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Are perpendicular

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Make equal angle with x-axis

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None of the above

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Solution

The correct option is A Are perpendicular
Line $4 x + 3 y = 24$ passes through the centre of the circle $(x - 3)^{2} + (y - 4)^{2} = 25$ and intersect the circle at points $(0, 8) and (6, 0)$ .
$∴$ the lines which are joining 0rigin to (0,8) and (6,0) are perpendicular.

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The condition that the straight line joining the origin to the points of intersection of the line 4x+3y=24 with the circle (x−3)2+(y−4)2=25.

The correct option is A Are perpendicularLine 4x+3y=24 passes through the centre of the circle(x−3)2+(y−4)2=25 and intersect the circle at points (0,8) and (6,0).∴ the lines which are joining 0rigin to (0,8) and (6,0) are perpendicular.

The condition that the straight line joining the origin to the points of intersection of the line $4 x + 3 y = 24$ with the circle $(x - 3)^{2} + (y - 4)^{2} = 25$ .

The correct option is A Are perpendicular
Line $4 x + 3 y = 24$ passes through the centre of the circle $(x - 3)^{2} + (y - 4)^{2} = 25$ and intersect the circle at points $(0, 8) and (6, 0)$ .
$∴$ the lines which are joining 0rigin to (0,8) and (6,0) are perpendicular.