Maths-
General
Easy
Question
If lx + my + n = 0 is a tangent to the parabola x2 = y, then condition of tangency is
- l2 = 2mn
- l = 4 m2 n2
- m2 =
- l2 = 4mn.
The correct answer is: l2 = 4mn.
To find the condition of tangency.
As we know, x=my+x touch the parabola
.
lx+my+n=0
![x equals fraction numerator negative m over denominator l end fraction y plus-or-minus n over l space t o u c h e s space x squared equals y space i f space fraction numerator negative n over denominator l end fraction equals fraction numerator begin display style 1 fourth end style over denominator begin display style fraction numerator negative m over denominator l end fraction end style end fraction
1 fourth equals fraction numerator m n over denominator l squared end fraction
l squared equals 4 m n](data:image/png;base64,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)
Therefore, the condition of tangency is = 4mn.
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rule, the value of
for the following data, is
![](data:image/png;base64,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)
Using Simpson’s
rule, the value of
for the following data, is
![](data:image/png;base64,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)
maths-General
maths-
A curve passes through the points given by the following table :
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/506990/1/977896/Picture4.png)
By Simpson’s rule, the area bounded by the curve, the x-axis and the lines x=1, x=4, is
A curve passes through the points given by the following table :
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/506990/1/977896/Picture4.png)
By Simpson’s rule, the area bounded by the curve, the x-axis and the lines x=1, x=4, is
maths-General
maths-
With the help of trapezoidal rule for numerical integration and the following table
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/508625/1/977890/Picture3.png)
the value of
is
With the help of trapezoidal rule for numerical integration and the following table
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/508625/1/977890/Picture3.png)
the value of
is
maths-General