11Number 23 can be done nicely for purpose of MCQS.
If K ≡ x+y =2
and L ≡ x-y=1
Change the origin to make L & K the X and Y-axes respectively.
Now the problem becomes damn simple, try it.
22. A straight line is drawn from the point(1,0) to the curve x2+y2+6x-10y+1=0, such that the intercept made on it by the curve subtends a right angle at the origin. Find the equations of the line.
23. Determine the range of values of φ ε [0,2λ] for which the point (cosθ,sinθ) lies inside the triangle formed by the lines x+y =2; x-y=1 & 6x+2y-√10=0.
3. Show that all the chords of the curve 3x2-y2-2x+4y=0 which subtend a right angle at the origin are cincurrent. Does this result also hold for the curve, 3x2+3y2-2x+4y=0? if yes, what is the point of concurrency & if not, give reasons.
4. The coordinates of the vertices of a quadrilateral are A(0,0); B(16,0),C(8,8),D(0,8). Find the equation of the line parallel to AC that halves the area of the quadrilateral in the form of y=mx+c.
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3 Answers
11
4CAN THIS BE A SOLUTION FOR 23 :
L1 : 0 + 0 - 2 < 0
cosθ + sinθ -2 < 0 => cosθ + sinθ < 2 ( 1)
L2 : 0 - 0 -1 < 0
cosθ - sinθ< 1 (2)
L3 : 0 + 0 - √10 < 0
6 COSθ + 2 SINθ < √10 (3)
Solving the three and getting a range of values for θ
1For 23 consider a unit circle sins the locus of all point costheta,sintheta is a unit circle centered at 0,0