Question

The number of integral points lying inside both the circle $x^2+y^2=20$ and the parabola $y^2=8x,$ is

• A. $19$
• B. $17$
• C. $20$
• D. $22$

Answer 1

The correct option is D $22$

x2+y2=20x2+8x−20=0x2−2x+10x−20=0x(x−2)+10(x−2)=0(x−2)(x+10)=0∴x=2or−10x2+y2=20x2+8x−20=0x2−2x+10x−20=0x(x−2)+10(x−2)=0(x−2)(x+10)=0∴x=2or−10 is only accepted

in such case only $(3,2),(1,2),(2,2),(3,2),(1,1),(2,1),(3,1),(4,1),(1,0),(2,0),(3,0),(4,0),(1,-1),(2,-1),(3,-1),(4,-1),(1,-2),(2,-2),(3,-2),(3,-3),(2,-3)$

lie in side the region so $22$