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question_answer1) The circle \[{{x}^{2}}\text{ }+{{y}^{2}}=5\] meets the parabola \[{{y}^{2}}=4x\] at P and Q, then find the length of PQ.
question_answer2) If \[P\left( at_{1}^{2}\,\,,\,\,2a{{t}_{1}} \right)\] and \[Q\left( at\,_{2}^{2},\,\,2a{{t}_{2}} \right)\] are two variable points on the curve \[{{y}^{2}}\text{ }=\text{ }4ax\] and PQ subtends a right angle at the vertex then find the value of \[{{t}_{1}}{{t}_{2}}\].
question_answer3) If one end of a focal chord of parabola \[{{y}^{2}}=16x\] is \[\left( 1,-4 \right).\] then find the length of the focal chord.
question_answer4) A focal chord of the parabola \[{{y}^{2}}=16x\] is tangent to the circle \[{{\left( x-6 \right)}^{2}}+\text{ }{{y}^{2}}=2\] then find sum of possible values of slope of this chord.
question_answer5) The line \[x-1=0\] is the directrix of the parabola \[{{y}^{2}}-kx+8=0.\] then find the product of values of k.
question_answer6) The equation of latus rectum of a parabola is \[x+y=8\] and the equation of the tangent at the vertex is \[x+y=12,\] if the length of the latus rectum is \[k\sqrt{2}\] then find k.
question_answer7) Find the latus rectum of the parabola \[{{y}^{2}}=4ax\] whose focal is PSQ such that \[SP=3\,\And \,\,SQ=2\] .
question_answer8) An equilateral triangle is inscribed in the parabola \[{{y}^{2}}=4ax,\] whose vertex is at the vertex of the parabola. If the length of its side is \[ka\sqrt{3}\] then find k.
question_answer9) If the distance between directrix and latus rectum of a parabola is 4 units, then find the length of its latus rectum.
question_answer10) Find the length of latus rectum of the parabola \[5{{y}^{2}}-3x-8y-1=0.\]
question_answer11) If the line \[y=3x+1\] touches parabola \[{{y}^{2}}=kx,\] then find k.
question_answer12) An equilateral triangle is inscribed in the parabola \[{{y}^{2}}=4ax\] with one vertex at the origin. The radius of the circum circle of that triangle is ka then find k.
question_answer13) The locus of the mid-point of the line segment joining the focus to a moving point on the parabola \[{{y}^{2}}=4ax\] is another parabola with the directrix \[x=\underline{\lambda }\] then find \[\lambda \].
question_answer14) Find the length of chord of the parabola \[{{y}^{2}}=4x\] which passes through the vertex and inclined at an angle \[60{}^\circ \] with x-axis.
question_answer15) Find the number of real tangents that can be drawn to the curve \[{{y}^{2}}+2xy+{{x}^{2}}+2x+3y+1=0\] From the point (1, -2).
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