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Equation of the tangent to the hyperbola 2x2 - 3y2 = 6 which is parallel to the line y = 3x + 4 is
  • a)
    y = 3x + 6
  • b)
    y = 3x - 4
  • c)
    y = 3x + 5 and y = 3x - 5
  • d)
    none of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Equation of the tangent to the hyperbola 2x2 - 3y2 = 6 which is parall...
Given equation of hyperbola is 2x2 - 3y2 = 6
Dividing by 6 we get



Therefore equations are:
y = 3x + 5
and y = 3x - 5
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Most Upvoted Answer
Equation of the tangent to the hyperbola 2x2 - 3y2 = 6 which is parall...
Given equation of hyperbola is 2x^2 - 3y^2 = 6.

To find the equation of tangent to the hyperbola which is parallel to the line y = 3x + 4.

Let the equation of tangent be y = mx + c.

Differentiating the given equation of hyperbola with respect to x, we get:

4x - 6y(dy/dx) = 0

dy/dx = (2x)/(3y)

Since the tangent is parallel to y = 3x + 4, its slope is 3.

Therefore, we have:

3 = (2x)/(3y)

y = (2x)/(9)

Substituting this value of y in the given equation of hyperbola, we get:

2x^2 - 3(4/81)x^2 = 6

x^2 = 243/50

x = ±(3√3)/5

Substituting these values of x in y = (2x)/(9), we get:

y = ±(2√3)/15

Therefore, the two points of intersection of the tangent with the hyperbola are:

(3√3)/5, (2√3)/15 and -(3√3)/5, -(2√3)/15

Using point-slope form of equation of a line, we get:

y - (2√3)/15 = 3(x - (3√3)/5)

Simplifying, we get:

y = 3x - 5

Hence, the equation of the tangent to the hyperbola which is parallel to the line y = 3x + 4 is y = 3x - 5. Therefore, option C is the correct answer.
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Equation of the tangent to the hyperbola 2x2 - 3y2 = 6 which is parallel to the line y = 3x + 4 isa)y = 3x + 6b)y = 3x - 4c)y = 3x + 5 and y = 3x - 5d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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Equation of the tangent to the hyperbola 2x2 - 3y2 = 6 which is parallel to the line y = 3x + 4 isa)y = 3x + 6b)y = 3x - 4c)y = 3x + 5 and y = 3x - 5d)none of theseCorrect answer is option 'C'. 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 Equation of the tangent to the hyperbola 2x2 - 3y2 = 6 which is parallel to the line y = 3x + 4 isa)y = 3x + 6b)y = 3x - 4c)y = 3x + 5 and y = 3x - 5d)none of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Equation of the tangent to the hyperbola 2x2 - 3y2 = 6 which is parallel to the line y = 3x + 4 isa)y = 3x + 6b)y = 3x - 4c)y = 3x + 5 and y = 3x - 5d)none of theseCorrect answer is option 'C'. Can you explain this answer?.
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