88365
What is the value of \(y\) so that the line through \((3, y)\) and \((2,7)\) is parallel to the line through (\(1,4)\) and \((0,6)\) ?
1 6
2 7
3 5
4 9
Explanation:
(D) : Let \(\mathrm{A}(3, \mathrm{y}), \mathrm{B}(2,7), \mathrm{C}(-1,4)\) and \(\mathrm{D}(0,6)\) be the given points. \(\mathrm{m}_{1}=\) slope of \(A B=\frac{7-y}{2-3}=(y-7)\) \(\mathrm{m}_{2}=\) slope of \(\mathrm{CD}=\frac{6-4}{0-(-1)}=2\) Since \(\mathrm{AB}\) and \(\mathrm{CD}\) are parallel. \(\therefore \mathrm{m}_{1}=\mathrm{m}_{2} \Rightarrow \mathrm{y}=9\).
BITSAT-2019
Co-Ordinate system
88368
A ray of light along \(x+3 \sqrt{y}=\sqrt{3}\) gets reflected upon reaching \(x\)-axis, the equation of the reflected ray is
1 \(\sqrt{3} y=x-\sqrt{3}\)
2 \(y=\sqrt{3} x-\sqrt{3}\)
3 \(\sqrt{3} y=x-1\)
4 \(y=x+\sqrt{3}\)
Explanation:
(A) : As the slope of incident ray is \(-\frac{1}{\sqrt{3}}\) So the slope of reflected ray has to be \(\frac{1}{\sqrt{3}}\). The point of incidence is \((\sqrt{3}, 0))\). Hence the equation of reflected ray is \(y=\frac{1}{\sqrt{3}}(x-\sqrt{3})\). \(\therefore \sqrt{3} \mathrm{y}-\mathrm{x}=-\sqrt{3} . \therefore \mathrm{x}-\sqrt{3} \mathrm{y}-\sqrt{3}=0\)
NEET Test Series from KOTA - 10 Papers In MS WORD
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Co-Ordinate system
88365
What is the value of \(y\) so that the line through \((3, y)\) and \((2,7)\) is parallel to the line through (\(1,4)\) and \((0,6)\) ?
1 6
2 7
3 5
4 9
Explanation:
(D) : Let \(\mathrm{A}(3, \mathrm{y}), \mathrm{B}(2,7), \mathrm{C}(-1,4)\) and \(\mathrm{D}(0,6)\) be the given points. \(\mathrm{m}_{1}=\) slope of \(A B=\frac{7-y}{2-3}=(y-7)\) \(\mathrm{m}_{2}=\) slope of \(\mathrm{CD}=\frac{6-4}{0-(-1)}=2\) Since \(\mathrm{AB}\) and \(\mathrm{CD}\) are parallel. \(\therefore \mathrm{m}_{1}=\mathrm{m}_{2} \Rightarrow \mathrm{y}=9\).
BITSAT-2019
Co-Ordinate system
88368
A ray of light along \(x+3 \sqrt{y}=\sqrt{3}\) gets reflected upon reaching \(x\)-axis, the equation of the reflected ray is
1 \(\sqrt{3} y=x-\sqrt{3}\)
2 \(y=\sqrt{3} x-\sqrt{3}\)
3 \(\sqrt{3} y=x-1\)
4 \(y=x+\sqrt{3}\)
Explanation:
(A) : As the slope of incident ray is \(-\frac{1}{\sqrt{3}}\) So the slope of reflected ray has to be \(\frac{1}{\sqrt{3}}\). The point of incidence is \((\sqrt{3}, 0))\). Hence the equation of reflected ray is \(y=\frac{1}{\sqrt{3}}(x-\sqrt{3})\). \(\therefore \sqrt{3} \mathrm{y}-\mathrm{x}=-\sqrt{3} . \therefore \mathrm{x}-\sqrt{3} \mathrm{y}-\sqrt{3}=0\)