


Get live Maths 1-on-1 Classs - Class 6 to 12
Miscellaneous
Misc 1 (b) Important Deleted for CBSE Board 2023 Exams
Misc 2 Important
Misc 3 Important
Misc 4 Deleted for CBSE Board 2023 Exams
Misc 5 Important Deleted for CBSE Board 2023 Exams
Misc 6 Important
Misc 7
Misc 8 Important
Misc 9 Important
Misc 10
Misc 11 Important
Misc 12 Important
Misc 13 Important
Misc 14 Important
Misc 15 Important
Misc 16
Misc 17 Important
Misc 18 Important
Misc. 19 (MCQ)
Misc 20 (MCQ) Important Deleted for CBSE Board 2023 Exams
Misc 21 (MCQ) Important You are here
Misc 22 (MCQ)
Misc. 23 (MCQ) Important
Misc 24 (MCQ) Important
Last updated at March 23, 2023 by Teachoo
Misc 21 The line 𝑦=𝑚𝑥+1 is a tangent to the curve 𝑦^2=4𝑥 if the value of 𝑚 is (A) 1 (B) 2 (C) 3 (D) 1/2Let (ℎ , 𝑘) be the point at which tangent is to be taken & Given Equation of tangent 𝑦=𝑚𝑥+1 & Curve is 𝑦^2=4𝑥 We know that Slope of tangent to the Curve is 𝑑𝑦/𝑑𝑥 𝑦^2=4𝑥 Misc 21 The line 𝑦=𝑚𝑥+1 is a tangent to the curve 𝑦^2=4𝑥 if the value of 𝑚 is (A) 1 (B) 2 (C) 3 (D) 1/2Let (ℎ , 𝑘) be the point at which tangent is to be taken Since (𝒉 , 𝒌) lies on line 𝑘=𝑚ℎ+1 Since (𝒉 , 𝒌) lies on curve 𝑘^2=4ℎ ℎ=𝑘^2/4 Putting (2) in (1) 𝑘=𝑚(𝒌^𝟐/𝟒)+1 4𝑘=𝑚𝑘^2+4 𝑚𝑘^2−4𝑘+4=0 Since tangent touches the curve at only one point There is only one value of k So, this quadratic equation has only one root Thus, Discriminant of Quadratic equation = 0 𝒃^𝟐−𝟒𝒂𝒄=𝟎 (−4)^2−4 × 𝑚 × 4=0 16−16𝑚=0 𝑚=16/16 𝑚=1 Hence Correct Answer is (A)