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Question

Through the point (3,4) are drawn two straight lines each inclined at 45 to the straight line xy=2. Find their equations and also find the area of triangle bounded by three lines.

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Solution

Given point: (3,4)
Given line: xy=2
i.e., y=x2 .........(A1)
Solution:
Plotting the given point & line
we have to find the equations of line A & B
The angle line A makes with x axis =45+ao
θa=45+ao
but a=45o- angle of inclination given in quetsion
θa=45+45=90o
The angle line B makes with x axis=45obo
θb=4545
θb=0
Slope of line A(mA)=tan1(θa)
=tan1(90)= ........(i)
Slope of line B(mb)=tan1(θb)
=tan1(0) ..........(ii)
=0
Equation of a line in slope point form is given as
(yy1)=m(xx1)
equation of line A is
(y4)=mA(x3)
(x3)=y4mA
x3=y4 by (i)
x3=0
x=3
equation of line A: x=3
i.e., x3=0 ........(ii)
Equation of line B is
(y4)=mB(x3)
(y4)=0(x3) by (ii)
equation of line B: y4=0
or y=4 ......(iv)
Equation of line A: x3=0
Equation of line B: y4=0
replotting the graph
Solving equation (iv) and A1
we get point p=6,4
Area of the triangle =12× base× height
=12×(41)×(63)
=12×3×3=92
The area of the triangle=4.5 sq. units.

1110482_827276_ans_69c98688b3f64e1d80785f081d2ea18c.jpg

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