Question

求直线3x-4y-5=0抛物线y^2=3x所得的弦长

Answer 1

3x=4y+5

代入抛物线

y^2-4y-5=0

(y-5)(y+1)=0

y=5,y=-1

y=5,x=(4y+5)/3=25/3

y=-1,x=(4y+5)/3=1/3

所以弦长=√[(1/3-25/3)^2+(-1-5)^2]

=√100

=10