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Question 1
The common tangent of the parabola
and
, is
![](https://gradeup-question-images.grdp.co/liveData/PROJ56965/1598010594969569.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ56965/1598010595704651.png)
Question 2
If the tangent at the point
to the parabola
meets the parabola
at
and
, then the mid point of
is
![](https://gradeup-question-images.grdp.co/liveData/PROJ56516/1597752172390219.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ56516/1597752173194690.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ56516/1597752173944325.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ56516/1597752174694938.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ56516/1597752175471650.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ56516/1597752176205831.png)
Question 3
The equation of a line touching both the parabolas
and
, is
![](https://gradeup-question-images.grdp.co/liveData/PROJ55108/1596541550705314.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ55108/15965415514362100.png)
Question 4
The real values of
for which the point
lies in the smaller region bounded by the circle
and the parabola
, is
![](https://gradeup-question-images.grdp.co/liveData/PROJ51443/1592808418208130.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ51443/1592808418927469.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ51443/1592808419643732.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ51443/1592808420359845.png)
Question 5
The axis of the parabola
:
![](https://gradeup-question-images.grdp.co/liveData/PROJ50851/1591618112300695.png)
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