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If lx+my+n=0 is a tangent to the parabola x2=y, then condition of tangency is
- a)l2=2mn
- b)l=4m2n2
- c)m2=4/n
- d)l2=4mn
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
If lx+my+n=0 is a tangent to the parabola x2=y, then condition of tang...
The given Line is lx + my + n = 0 and the parabola x2 = y
Eliminating x from these equation, we get
or m2y2 + n2 + 2 myn = l2 y
or m2y2 + (2mn - l2)y + n2 = 0
if the line touches the parabola, then the roots of the equation will be equal.
i.e (2mn - l2)2 - 4.m2n2 = 0
or 4.m2n2 + l4 - 4mn.l2 - 4.m2n2 = 0
or l4 - 4mnl2 = 0
or l2 (l2 - 4mn) = 0
or l2 - 4mn = 0
or l2 = 4mn
Eliminating x from these equation, we get
or m2y2 + n2 + 2 myn = l2 y
or m2y2 + (2mn - l2)y + n2 = 0
if the line touches the parabola, then the roots of the equation will be equal.
i.e (2mn - l2)2 - 4.m2n2 = 0
or 4.m2n2 + l4 - 4mn.l2 - 4.m2n2 = 0
or l4 - 4mnl2 = 0
or l2 (l2 - 4mn) = 0
or l2 - 4mn = 0
or l2 = 4mn
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Community Answer
If lx+my+n=0 is a tangent to the parabola x2=y, then condition of tang...
The given Line is lx + my + n = 0 and the parabola x2 = y
Eliminating x from these equation, we get
or m2y2 + n2 + 2 myn = l2 y
or m2y2 + (2mn - l2)y + n2 = 0
if the line touches the parabola, then the roots of the equation will be equal.
i.e (2mn - l2)2 - 4.m2n2 = 0
or 4.m2n2 + l4 - 4mn.l2 - 4.m2n2 = 0
or l4 - 4mnl2 = 0
or l2 (l2 - 4mn) = 0
or l2 - 4mn = 0
or l2 = 4mn
Eliminating x from these equation, we get
or m2y2 + n2 + 2 myn = l2 y
or m2y2 + (2mn - l2)y + n2 = 0
if the line touches the parabola, then the roots of the equation will be equal.
i.e (2mn - l2)2 - 4.m2n2 = 0
or 4.m2n2 + l4 - 4mn.l2 - 4.m2n2 = 0
or l4 - 4mnl2 = 0
or l2 (l2 - 4mn) = 0
or l2 - 4mn = 0
or l2 = 4mn
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If lx+my+n=0 is a tangent to the parabola x2=y, then condition of tangency isa)l2=2mnb)l=4m2n2c)m2=4/nd)l2=4mnCorrect answer is option 'D'. Can you explain this answer?
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If lx+my+n=0 is a tangent to the parabola x2=y, then condition of tangency isa)l2=2mnb)l=4m2n2c)m2=4/nd)l2=4mnCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If lx+my+n=0 is a tangent to the parabola x2=y, then condition of tangency isa)l2=2mnb)l=4m2n2c)m2=4/nd)l2=4mnCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If lx+my+n=0 is a tangent to the parabola x2=y, then condition of tangency isa)l2=2mnb)l=4m2n2c)m2=4/nd)l2=4mnCorrect answer is option 'D'. Can you explain this answer?.
If lx+my+n=0 is a tangent to the parabola x2=y, then condition of tangency isa)l2=2mnb)l=4m2n2c)m2=4/nd)l2=4mnCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If lx+my+n=0 is a tangent to the parabola x2=y, then condition of tangency isa)l2=2mnb)l=4m2n2c)m2=4/nd)l2=4mnCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If lx+my+n=0 is a tangent to the parabola x2=y, then condition of tangency isa)l2=2mnb)l=4m2n2c)m2=4/nd)l2=4mnCorrect answer is option 'D'. Can you explain this answer?.
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