Question is in the image Recall the equation for a circle with center (h, k) and radius r. At what point in the first quadrant does theline with equation y = 0.5x +1 intersect the circle with radius 3 and center (0, 1)?I%3DEnter your answer correct to 3 decimal places.Check Answer

Name: Question is in the image Recall the equation for a circle with center
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Question is in the image Recall the equation for a circle with center (h, k) and radius r. At what point in the first quadrant does theline with equation y = 0.5x +1 intersect the circle with radius 3 and center (0, 1)?I%3DEnter your answer correct t

Given that the equation of line, y=0.5x+1 .........(1) The standard equation of circle having center (h, k) and radius “r” is, x-h2+y-k2=r2Here, h,k=0,1 and r=3 then,x-02+y-12=32x2+y2+1-2y=9x2+y2-2y+1-9=0x2+y2-2y-8=0 .........(2) Substitute y=0.5x+1 in equation (2) then, x2+0.5x+12-20.5x+1-8=0x2+0.25x2+1+x-x-2-8=01.25x2-9=01.25x2=9Further solving it,x2=91.25x2=900125x=±900125=±3055x=-65, 65In first quadrant take,x=65To sketch the graph,