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Question 528215: can you please help me solve these problems on parabolas and circles? Thanks
1.Find the equation of the two tangents to the parabola y^2=5x from the point (-1,1).
2.Find the equation of the two tangents,drawn through the external points (11,3) to the circle x^2+y^2=40.
3.write the equations of the tangent to the parabola y^2=10x,at the extremities of the latus recum.on what line do these tangent intersect?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! can you please help me solve these problems on parabolas and circles? Thanks
1.Find the equation of the two tangents to the parabola y^2=5x from the point (-1,1).
2.Find the equation of the two tangents,drawn through the external points (11,3) to the circle x^2+y^2=40.
3.write the equations of the tangent to the parabola y^2=10x,at the extremities of the latus recum.on what line do these tangent intersect.
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1.Find the equation of the two tangents to the parabola y^2=5x from the point (-1,1).
y^2=5x
x=y^2/5
point slope formula: y-y1=m(x-x1)
For given problem:
y-1=m(x+1)
y-1=mx+m
y-1=m((y^2)/5)+1)
y-1=(m/5)y^2+m
(m/5)y^2+m-y+1=0
a=m/5, b=-1, c=(m+1)
b^2-4ac=1-4*(m/5)(m+1)
=1-(4/5)m^2-(4/5)m
=.8m^2+.8m-1=0
a=.8, b=.8, c=-1
m=[-.8±√(.8^2-4*.8*-1)]/2*.8
m=[-.8±√3.84]/1.6
m=(-.8±1.96)/1.6
m=-1.72
or
m=.724
Equation of line:
y=mx+b
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y=-1.72x+b
solve for b using given point (-1,1)
1=-1.72*-1+b
b=-.72
equation: y=-1.72x-.72
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y=.724x+b
solve for b using given point (-1,1)
1=.724*-1+b
b=1.724
equation: y=.724x+1.724
see graph below as a visual check on the answers
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y=±(5x)^.5
note to student: Please submit other two problems separately.
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