Question

if the line 3x-4y+5=0 is a tangent to the parabola y^2=4ax then a is equal

Answer 1

Answer:

The value of a is 15/16

Step-by-step explanation:

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The solution is simple and easy to understand.

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Answer 2

The value of a is 15/16

Step-by-step explanation:

The given equation for line is

3x - 4y + 5 = 0

Convert this equation to slope intercept form of a line y = mx + b

$3x - 4y + 5 = 0\\\\4y=3x+5\\\\y=\frac{3}{4}x+\frac{5}{4}$

Comparing this equation with y = mx + b, we get

$m=\frac{3}{4}, b = \frac{5}{4}$

Now, the condition that the line y = mx +b is tangent with the parabola y² = 4ax is

$b=\frac{a}{m}$

Substituting the known values, we get

$\frac{5}{4}=\frac{a}{\frac{3}{4}}\\\\\frac{5}{4}=\frac{4a}{3}$

Cross multiplying, we get

$16a=15$

Divide both sides by 16

$a=\frac{15}{16}$

Therefore, the value of a is 15/16

#Learn More:

Y=3x+c is a tangent to the circle x^2+y^2-2x-4y -5=0 , then c is =?

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