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The locus of a point from which 3 normals can be drawn to y2=4x such that the sum of the angles made by them with the axis is 3pie/4 is a
a) parabola
b) circle
c) straight line
d) none of these
Dear student,
Write the equation of normal to parabola.
Normal at the Point (x1, y1 ): The equation of the tangent at the point (x1, y1) is yy1 = 2a(x + x1). Since the slope of tangent = 2a/y1 , slope of normal is -y1/ 2a . Also it passes through (x1, y1). Hence its equation is y - y1 = y1 / 2a ( x - x1 ) . . . . . (i) Normal in Terms of m: In equation (i), put - y1 / 2a = m so that y1 = -2am and x1 = y12 / 4a = am2, then the equation becomes y = mx - 2am - am3 . . . . . (ii) where m is a parameter. Equation (ii) is the normal at the point (am2, -2am) of the parabola. Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation. All the best. Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian. Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar respectively : Click here to download the toolbar.. Askiitians Expert Sagar Singh B.Tech, IIT Delhi sagarsingh24.iitd@gmail.com
Normal at the Point (x1, y1 ):
The equation of the tangent at the point (x1, y1) is yy1 = 2a(x + x1). Since the slope of tangent = 2a/y1 , slope of normal is -y1/ 2a . Also it passes through (x1, y1).
Hence its equation is y - y1 = y1 / 2a ( x - x1 ) . . . . . (i)
Normal in Terms of m:
In equation (i), put - y1 / 2a = m so that y1 = -2am and x1 = y12 / 4a = am2, then the equation becomes
y = mx - 2am - am3 . . . . . (ii)
where m is a parameter. Equation (ii) is the normal at the point (am2, -2am) of the parabola.
Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation. All the best. Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian. Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar respectively : Click here to download the toolbar.. Askiitians Expert Sagar Singh B.Tech, IIT Delhi sagarsingh24.iitd@gmail.com
Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation.
All the best.
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Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar respectively : Click here to download the toolbar..
Askiitians Expert
Sagar Singh
B.Tech, IIT Delhi
sagarsingh24.iitd@gmail.com
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